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Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals...
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Transcript of Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals...
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 2
Goals
I can find the sine, cosine, and tangent of an acute angle.
I can solve problems using trigonometric ratios.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 3
Terminology
No one, uses the word trigonometry.
It’s
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 4
What is trig?
Literally, the measure of triangles. An extremely useful, practical and
powerful math tool. A branch of math that finds its way into
practically everything we do. Usually learned in high school.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 5
What you will learn…
The basic terms and methods of solving right triangles.
How to solve problems using trig.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 6
Trig Ratios
Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 7
Right Triangle
Hypotenuse
Leg
Leg
A
From A, this leg is the Adjacent side.
From A, this leg is the Opposite side.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 8
Right Triangle
Hypotenuse
Leg
Leg
A
From A, this leg is the Adjacent side.
From A, this leg is the Opposite side.
B
From B, this leg is the Adjacent side.
From B, this leg is the Opposite side.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 9
Right Triangle
Hypotenuse
Adjacent
Opposite
A
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 10
Trig Ratio Definition: Sine
Hypotenuse
Adjacent
Opposite
A
Sine of A = Opposite
Hypotenuse
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 11
Trig Ratio Definition: Cosine
Hypotenuse
Adjacent
Opposite
A
Cosine of A = Adjacent
Hypotenuse
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 12
Trig Ratio Definition: Tangent
Hypotenuse
Adjacent
Opposite
A
Tangent of A = OppositeAdjacent
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 13
Abbreviations
Tangent of A = OppositeAdjacent
Sine of A = Opposite
Hypotenuse
Cosine of A = Adjacent
Hypotenuse
sin A
cos A
tan A
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 14
Memory Aid
Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent.
SOHCAHTOA
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 15
Writing Ratios SOHCAHTOA
4sin
53
cos54
tan3
B
B
B
3
4
5
A
B 3sin
54
cos53
tan4
A
A
A
?
??
??
?
?
??
??
?
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 16
Find these values using your calculator—Make sure you’re in Degree Mode!!!
SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN 90
.2588 .7071 1 .1736 .1736 .0875 .5 1
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 17
Solving Triangles
Carefully analyze what given information you have.
Decide what you are trying to find. Ask: how do you use the given
information to solve the problem? WRITE AN EQUATION. (SOHCAHTOA)
Solve.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 18
Example 1 Find x.
28
x 15
From the 28 angle, x is the ?
Opposite side,
and 15 is the
Hypotenuse.
What trig ratio is this?
Sine (SOHCAHTOA)
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 19
Example 1 Find x.
sin 2815
15sin 28
15(.4695)
7.0
x
x
x
x
28
x 15
Write the equation and solve.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 20
Example 2 Find y.
cos3156
56cos31
56(.8572)
48.0
y
y
y
y
31y
56
Write the equation and solve.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 21
Example 3 Find a.
tan 408
8tan 40
8(.8391)
6.7
a
a
a
a
40
a
8
Write the equation and solve.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 22
Algebra Reminder
Solve: 123
12 3
12 3
3 34
xx
x
x
a ac b
b c
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 23
Example 4 Find a.
17tan 40
tan 40 17
17 17
tan 40 .839120.3
aa
a
x
40a
17
Write the equation and solve.
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 24
Example 5 Find x & y.
tan 78150
150 tan 78
150(4.7046)
705.7
x
x
x
x
78
x y
150
150cos78
150 150
cos78 .2079721.5
y
y
y
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 25
Angle of Elevation
Horizontal
Angle of Elevation
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 26
Angle of DepressionHorizontal
Angle of Depression
(.wav)
April 18, 2023 Geometry 9.5 Trigonometric Ratios w/o Calculator 27
Problem
30 yd15
h
Standing 30 yards from a tree, the angle of elevation to the top of the tree is 15. How tall is the tree?
tan1530
30 tan15
30(.2679)
8.0
h
h
h
h