The Lions Field
-
Upload
kaylaap -
Category
Entertainment & Humor
-
view
446 -
download
2
description
Transcript of The Lions Field
The Lions Field
Ajani's Notebook:
Ajani only knew a few pieces of information which he had to use to solve how far he needed to walk to reach Eagle Rock. He could only go west or east because crossing the field would be too dangerous for the lamb. He also needed to know how fast he had to travel to reach Eagle Rock in two days time.
To organize what he knew Ajani made a list with a corresponding drawing:
The approximate placement of Eagle Rock was NE of his village
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
The approximate placement of Eagle Rock was NE of his village
Eagle Rock
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
Eagle Rock
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
Eagle Rock
9km
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Turn 70° N of E
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
Eagle Rock
9km
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Turn 70° N of E
Ajani’s List: The Eastern PathAjani’s List: The Eastern Path
70°
9km
Eagle Rock
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Turn 70° N of E
To reach Eagle Rock travel West
70°
9km
Ajani’s List: The Eastern Ajani’s List: The Eastern PathPath
Eagle Rock
The approximate placement of Eagle Rock was NE of his village
To take the eastern route he needed to travel east 9km
Turn 70° N of E
To reach Eagle Rock travel West
70°
9km
Ajani’s List: The Eastern Ajani’s List: The Eastern PathPath
Eagle Rock
70°
9km
Ajani’s List: Other KnownsAjani’s List: Other Knowns
Eagle Rock
To cross the field diagonally NE and intersect the 70° N of E path it was a 20km journey
70°
9km
20km
Ajani’s List: Other KnownsAjani’s List: Other Knowns
Eagle Rock
To cross the field diagonally NE and intersect the 70° N of E path it was a 20km journey
Step 1: Label the diagram
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
Step 1: Label the diagram
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
Step 1: Label the diagram
Step 2: Solve for Angle A
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
Something to Think About;Something to Think About;
The total degree measurement of a straight line is 180°
Something to Think About;Something to Think About;
180°
The total degree measurement of a straight line is 180°
Step 1: Label the diagram
Step 2: Solve for Angle A
Since a straight line is equal to 180 °
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
Step 1: Label the diagram
Step 2: Solve for Angle A
Since a straight line is equal to 180 °
Angle A = 180 ° - 70 ° Angle A = 110 °
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
Step 1: Label the diagram
Step 2: Solve for Angle A
Since a straight line is equal to 180 °
Angle A = 180 ° - 70 ° Angle A = 110 °
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
There are two equations that may be used to solve for non-right angle triangles:
Something to Think About;Something to Think About;
There are two equations that may be used to solve for non-right angle triangles:
Something to Think About;Something to Think About;
The Sine Law Equation:
•Takes the Sine of an angle and divides it by the corresponding angles side
•Is used when three pieces of information is known
•Is not compatible with Side-Angle-Side or Side-Side-Side triangles
There are two equations that may be used to solve for non-right angle triangles:
Something to Think About;Something to Think About;
•Is with Side-Angle-Side or Side-Side-Side triangles
•Isn’t recommended because tedious work
The Cosine Law Equation:
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
And divide by 20 to isolate Sin C:
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
And divide by 20 to isolate Sin C:
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
And divide by 20 to isolate Sin C:
Solve and take the inverse Sin to calculate the angle.
Step 3: Solve for Angle C
Side c is known therefore Angle C can be solved for with the Sine Equation
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
To solve for angle C cross multiply:
And divide by 20 to isolate Sin C:
Solve and take the inverse Sin to calculate the angle.
25.02°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
The sum of all three angles in a triangle is equal to 180°
Something to Think About;Something to Think About;
A
B C
Therefore: A+B+C=180°
Step 4: Solve for Angle B
Angle B can be solved for by subtracting Angles A and C from 180°
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
Step 4: Solve for Angle B
Angle B can be solved for by subtracting Angles A and C from 180°
Angle B = 180° - (110° + 25.02°) = 44.98°
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
It is always best to use information originally given in a question to solve for
other unknowns
Something to Think About;Something to Think About;
•There has not been previous rounding
•More accuracy
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
Cross multiple and divide to isolate b:
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
Cross multiple and divide to isolate b:
44.98°
Step 5: Solve for Side b
Now that angle B is known side b can be calculated using the Sine Equation.
70°
9km
20km
Eagle Rock
Solving the TriangleSolving the Triangle
a
b
c
AB
C
110 °
25.02°
Cross multiple and divide to isolate b:
15.04 km
44.98°
Ajani’s List: Other KnownsAjani’s List: Other Knowns•Eagle Rock is 72° N of E from the village
70°
9km
20km
Eagle Rock
a
b
c
AB
C
110 °
25.02°
15.04 km
44.98°
Ajani’s List: Other KnownsAjani’s List: Other Knowns•Eagle Rock is 72° N of E from the village
70°
9km
20km
Eagle Rock
a
b
c
AB
C
110 °
25.02°
15.04 km
72°
44.98°
70°
9km
20km
Eagle Rock
a
b
c
AB
C
110 °
25.02°
15.04 km
72°
44.98°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
AB
C
110 °
25.02°
15.04 km
72°
44.98°
Step 6: Re-label new triangle
Since both triangles share:
•A Common Side : a
•Common Angles: C and B
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
AB
C
110 °
25.02°
15.04 km
72°
44.98°
Step 6: Re-label new triangle
Since both triangles share:
•A Common Side : a
•Common Angles: C and B
The rest of the triangle can be labeled based on these three pieces of information.
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
Step 6: Re-label new triangle
Since both triangles share:
•A Common Side : a
•Common Angles: C and B
The rest of the triangle can be labeled based on these three pieces of information.
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Step 7: Solve for Angle B
Solving the TriangleSolving the Triangle
Step 7: Solve for Angle B
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
Step 7: Solve for Angle B
Both the 72° and 44.98 ° angles begin on the same axis then:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
Step 7: Solve for Angle B
Both the 72° and 44.98 ° angles begin on the same axis then:
Angle B= 72° - 44.98°
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
110 °
25.02°
15.04 km
72°
44.98°
Step 7: Solve for Angle B
Both the 72° and 44.98 ° angles begin on the same axis then:
Angle B= 72° - 44.98°
Angle B= 27.02°
Solving the TriangleSolving the Triangle
27.02 °
When a transversal line passes through two parallel lines corresponding angles are formed.
Something to Think About;Something to Think About;
When a transversal line passes through two parallel lines corresponding angles are formed.
This means that the angles on alternate sides of the transversal are the same.
Something to Think About;Something to Think About;
When a transversal line passes through two parallel lines corresponding angles are formed.
This means that the angles on alternate sides of the transversal are the same.
Something to Think About;Something to Think About;
When a transversal line passes through two parallel lines corresponding angles are formed.
This means that the angles on alternate sides of the transversal are the same.
Something to Think About;Something to Think About;
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Step 7: Solve for Angle B
Step 8: Solve for Angle C
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
Step 8: Solve for Angle C
Side a is a transversal line
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
Step 8: Solve for Angle C
Side a is a transversal line
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
Step 8: Solve for Angle C
Side a is a transversal line
This means that Angle C is congruent to 44.98°
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
Step 8: Solve for Angle C
Side a is a transversal line
This means that Angle C is congruent to 44.98° this is because it is on the alternate side of the transversal line to the original 44.98°.
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
44.98°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Step 7: Solve for Angle B
Step 8: Solve for Angle C
Step 9: Solve for Angle A
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°
44.98°
27.02 °
15.04 km
Step 9: Solve for Angle A
Since two angles are known:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
44.98°
Step 9: Solve for Angle A
Since two angles are known:
Angle A = 180 ° - (44.98° + 27.02°)
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
44.98°
Step 9: Solve for Angle A
Since two angles are known:
Angle A = 180 ° - (44.98° + 27.02°)
Angle A = 108°
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
44.98°108°
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Step 7: Solve for Angle B
Step 8: Solve for Angle C
Step 9: Solve for Angle A
Step 10: Solve for Side b
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108°
Cross multiply and divide to isolate b
44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108°
Cross multiply and divide to isolate b
44.98°
Step 10: Solve for Side b
The Sine equation can be used to solve side b:
Solving the TriangleSolving the Triangle
70°
9km
20km
Eagle Rock
a
b
c
A
B
C
72°27.02 °
15.04 km
108°
Cross multiply and divide to isolate b
44.98°
9.55km
Step 1: Label the diagram
Step 2: Solve for Angle A
Step 3: Solve for Angle C
Step 4: Solve for Angle B
Step 5: Solve for Side b
Step 6: Re-label new triangle
Step 7: Solve for Angle B
Step 8: Solve for Angle C
Step 9: Solve for Angle A
Step 10: Solve for Side b
Step 11: Solve the Eastern Route
Solving the TriangleSolving the Triangle
70°
9km
20km
ac
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Eagle Rockb 9.55km
Step 11: Solve the Eastern Route
To Solve for the entire distance of the eastern route:
Solving the TriangleSolving the Triangle
70°
9km
20km
ac
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Eagle Rockb 9.55km
Step 11: Solve the Eastern Route
To Solve for the entire distance of the eastern route:
Eastern Route= 9km+15.04km+9.55km
Solving the TriangleSolving the Triangle
70°
9km
20km
ac
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Eagle Rockb 9.55km
Step 11: Solve the Eastern Route
To Solve for the entire distance of the eastern route:
Eastern Route= 9km+15.04km+9.55km
Eastern Route= 33.59km
Solving the TriangleSolving the Triangle
70°
9km
20km
ac
A
B
C
72°27.02 °
15.04 km
108° 44.98°
Eagle Rockb 9.55km
•The path to the west was 50° N of W.
70°
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
Ajani’s List: The Western Ajani’s List: The Western PathPath
•The path to the west was 50° N of W.
70°
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
Ajani’s List: The Western Ajani’s List: The Western PathPath
50°
•The path to the west was 50° N of W.•Eagle Rock is directly East from the first path
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
Ajani’s List: The Western Ajani’s List: The Western PathPath
50°
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Something to Think About;Something to Think About;
ac
A
B
Cb
When working with multiple triangles:
•the side of a previous triangle
Something to Think About;Something to Think About;
ac
A
B
Cb
When working with multiple triangles:
•the side of a previous triangle
•Can be used as the side of another triangle
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Cross multiply and divide to isolate c
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Cross multiply and divide to isolate c
Step 1: Solve Side c
20km
ac
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Cross multiply and divide to isolate c
Step 1: Solve Side c
20kma
c
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
Side c can be solved using the Sine Formula and values from the previous triangle:
Cross multiply and divide to isolate c
14.86km
c= 14.864729… = 14.86km
Step 1: Solve Side cStep2: Solve Angle A
20km
c
A
B
72°27.02 °
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
Step2: Solve Angle A
Angle A is on the same horizontal line as the Angle of 108°
20km
c
A
B
72°27.02 °
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
Step2: Solve Angle A
Angle A is on the same horizontal line as the Angle of 108°
Therefore Angle A = 180 °-108 °
20km
c
A
B
72°27.02 °
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
Step2: Solve Angle A
Angle A is on the same horizontal line as the Angle of 108°
Therefore Angle A = 180 °-108 °Angle A = 72°
20kma
c
A
B
C
72°27.02 °
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
14.86km
72°
Step 1: Solve Side cStep 2: Solve Angle AStep 3: Solve Angle B
20km
c
A
B
72°27.02 °
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
72°
Step 3: Solve Angle B
Since the angles of 50° and 72° are both located on the x axis subtracting these from 180° will give the value of Angle B.
20km
c
A
B
72°
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
72°
Step 3: Solve Angle B
Since the angles of 50° and 72° are both located on the x axis subtracting these from 180° will give the value of Angle B.
Angle B= 180° - (50°+72°)20km
c
A
B
72°
108° 44.98°
Eagle Rock
50°
Solving the TriangleSolving the Triangle
14.86km
a
C b
72°
Step 3: Solve Angle B
Since the angles of 50° and 72° are both located on the x axis subtracting these from 180° will give the value of Angle B.
Angle B= 180° - (50°+72°)Angle B= 58° 20km
a
c
A
B
C
72°
108° 44.98°
Eagle Rockb
50°
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Step 1: Solve Side cStep 2: Solve Angle AStep 3: Solve Angle BStep 4: Solve Angle C
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Step 4: Solve Angle C
Since we know a triangle is equal to 180°
Angle C= 180° - (58°+72°)
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
72°
58°
Step 4: Solve Angle C
Since we know a triangle is equal to 180°
Angle C= 180° - (58°+72°)Angle C= 50°
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
72°
58°
50°
Step 4: Solve Angle C
Since we know a triangle is equal to 180°
Angle C= 180° - (58°+72°)Angle C= 50°
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
72°
58°
50°
**Note to check if your angles are correct:
Angle B plus 50° should equal 108° because it is on the alternate side of the transversal c.
50 ° + 58 ° = 108 °
108°
Step 1: Solve Side cStep 2: Solve Angle AStep 3: Solve Angle BStep 4: Solve Angle CStep 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate a
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate a
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate a
Step 5: Solve side a
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate a
a= 18.448929…
= 18.45km
18.45km
Step 1: Solve Side cStep 2: Solve Angle AStep 3: Solve Angle BStep 4: Solve Angle CStep 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
18.45km
Step 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
18.45km
Step 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
18.45km
Step 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate b 18.45k
m
Step 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate b 18.45k
m
Step 5: Solve Side b
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving the TriangleSolving the Triangle
14.86km
58°
72°
Cross multiply and divide to isolate b
b= 16.450735…
= 16.45km
16.45km
18.45km
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving for the Western Solving for the Western RouteRoute
14.86km
58°
72°
16.45km
18.45km
To solve for the Western Route from the village to Eagle Rock:
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving for the Western Solving for the Western RouteRoute
14.86km
58°
72°
16.45km
18.45km
To solve for the Western Route from the village to Eagle Rock:
Add the two paths:
Western Route= 18.45+16.45
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Solving for the Western Solving for the Western RouteRoute
14.86km
58°
72°
16.45km
18.45km
To solve for the Western Route from the village to Eagle Rock:
Add the two paths:
Western Route= 18.45+16.45
Western Route= 34.90
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Choosing the Shortest RouteChoosing the Shortest Route
14.86km
58°
72°
16.45km
18.45km 15.04 km
9.55km
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Choosing the Shortest RouteChoosing the Shortest Route
14.86km
58°
72°
16.45km
18.45km 15.04 km
9.55kmRoute One = 9km + 15.04km + 9.55km
= 33.59km
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Choosing the Shortest RouteChoosing the Shortest Route
14.86km
58°
72°
16.45km
18.45km 15.04 km
9.55kmRoute One = 9km + 15.04km + 9.55km
= 33.59km
Route Two= 18.45km + 16.45km
= 34.90km
20kma
c
A
B
C
72°
108° 44.98°
Eagle Rockb
Choosing the Shortest RouteChoosing the Shortest Route
14.86km
58°
72°
16.45km
18.45km 15.04 km
9.55kmRoute One = 9km + 15.04km + 9.55km
= 33.59km
Route Two= 18.45km + 16.45km
= 34.90km
According to Ajani’s calculations route one would be the shortest path to Eagle Rock.
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has walking to complete the journey how long will it take to travel the 33.59 km?
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?Step one: set up a ratio to use to calculate the speed
Since Ajani is going to be walking for 12 hours each day for two days you need to know how far he will be able to walk in 24 hours.
Cross multiply and divide to isolate the value of the km.
Km= 36km
Since Ajani only has to travel 33.59km he will be able to walk at a normal pace since he will be able to cover 36km in 24 hours.
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?
Step one: set up a ratio to use to calculate the speed
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?Step one: set up a ratio to use to calculate the speed
Since Ajani is going to be walking for 12 hours each day for two days you need to know how far he will be able to walk in 24 hours.
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?Step one: set up a ratio to use to calculate the speed
Since Ajani is going to be walking for 12 hours each day for two days you need to know how far he will be able to walk in 24 hours.
Cross multiply and divide to isolate the value of the km.
Km= 36km
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?Step one: set up a ratio to use to calculate the speed
Since Ajani is going to be walking for 12 hours each day for two days you need to know how far he will be able to walk in 24 hours.
Cross multiply and divide to isolate the value of the km.
Km= 36km
SpeedSpeedAjani needs to know if he walks at a speed of 1.5km per hour and is planning to spend only 12 hours of each day of the two days he has to complete the journey how long will it take to travel the 33.59 km?Step one: set up a ratio to use to calculate the speed
Since Ajani is going to be walking for 12 hours each day for two days you need to know how far he will be able to walk in 24 hours.
Cross multiply and divide to isolate the value of the km.
Km= 36km
Since Ajani only has to travel 33.59km he will be able to walk at a normal pace since he will be able to cover 36km in 24 hours.