Congruency and Triangles Featuring Right Triangles Section 4.6.
Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right...
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Transcript of Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right...
Solving Right Triangles9.6
Chapter 9Right Triangles and Trigonometry
Section 9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Solving Right Triangles9.6
Solving Right TrianglesCONCEPT
SUMMARY
SOLVE RIGHT TRIANGLES
To Solve A Right Triangle: Determine the measure of all three angles and the length of all three sides.
a
C
B
ab
c
1. Three Angles
A, B, C
2. Three Sides
• a, b, c
Solving Right Triangles9.6
Example 1 Given 1 Side and 1 Angle
Example 2 Given 2 Sides
Example 3 Solving Real Life Problems
Homework
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
X & Y are Complements
mX + mY =90
71 + mY =90
mY = 19
1910.4
30.3
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
Find AB, AC, mA
1952tan
AB
AB52tan19
AB 24.319
AC19
52cos
19)52(cos AC
52cos19AC
mA + mC = 90
mA + 52 = 90
mA = 3830.861AC
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
mN = 55
sin359
MN MN 5.162
cos359
LM LM 7.372
Solving a Right Triangle Given 1 Side, 1 Angle
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
=12
125
tan 1B 22.62
mA + mB = 90
mA + 33.69 =90
mA 67.38
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Use the Pythagorean theorem to find XZ
(XZ)2 + 142 = 252
(XZ)2 + 196 = 225
(XZ)2 = 29
29XZ
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Need to find X
2514
sin X
X
2514
sin 1
mX 34.06
mX + mY = 90
34.06 + mY = 90
mY 55.94
Solving Right Triangles9.6
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
340 2 85 18.439ML
1 12tan 40.601
14m M
49.399m L
CIRCUS ACTS At the circus, a person in the audience watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat isMake a drawing.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet, QS is 30.5 feet. Let x represent PQ.
Multiply both sides by x.
Divide both sides by tan
Simplify.
Answer: The audience member is about 60 feet from the base of the platform.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
SHORT-RESPONSE TEST ITEM A wheelchair ramp is 3 meters long and inclines at Find the height of the ramp to the nearest tenth centimeter.
Solve the Test ItemMethod 1The ground and the horizontal level with the platform to which the ramp extends are parallel. Therefore,
since they are alternate interior angles.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Answer: The height of the ramp is about 0.314 meters,
Mulitply each side by 3.
Simplify.
Y
W
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
SHORT-RESPONSE TEST ITEM A roller coaster car is at one of its highest points. It drops at a angle for 320 feet. How high was the roller coaster car to the nearest foot before it began its fall?
Answer: The roller coaster car was about 285 feet above the ground.
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS