1. Chapter 9 Right Triangles and Trigonometry
Section 9.6
Solving Right Triangles
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

2. SOLVE RIGHT TRIANGLES
Solving Right Triangles
CONCEPT
SUMMARY
To Solve A Right Triangle: Determine the measure of all three angles and the length of all three sides. a C B b c
Three Angles
A, B, C
Three Sides
a, b, c

3. Example 1 Given 1 Side and 1 Angle Example 2 Given 2 Sides
SOLVE RIGHT TRIANGLES
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
Example 1 Given 1 Side and 1 Angle
Example 2 Given 2 Sides
Example 3 Solving Real Life Problems
Homework

4. Solving a Right Triangle Given 1 Side, 1 Angle
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
10.4 19
30.3
X & Y are Complements
mX + mY =90
71 + mY =90
mY = 19

5. Solving a Right Triangle Given 1 Side, 1 Angle
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
Find AB, AC, mA
mA + mC = 90
mA + 52 = 90
mA = 38
AB 

6. Solving a Right Triangle Given 1 Side, 1 Angle
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 1 Side, 1 Angle
mN = 55
MN  5.162
LM  7.372

7. Solving a Right Triangle Given 2 Sides
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides

8. Solving a Right Triangle Given 2 Sides
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
=12
mA + mB = 90
mA =90
mA  67.38
 22.62

9. Solving a Right Triangle Given 2 Sides
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Use the Pythagorean theorem to find XZ
(XZ) = 252
(XZ) = 225
(XZ)2 = 29

10. Solving a Right Triangle Given 2 Sides
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides
Need to find X
mX + mY = 90
mY = 90
mY  55.94
mX  34.06

11. Solving a Right Triangle Given 2 Sides
SOLVE RIGHT TRIANGLES
Solving a Right Triangle Given 2 Sides

12. USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS
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 is
Make a drawing.

13. Multiply both sides by x.
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.

14. 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 Item Method 1 The ground and the horizontal level with the platform to which the ramp extends are parallel. Therefore, since they are alternate interior angles.

15. Answer: The height of the ramp is about 0.314 meters,
USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS Y W
Mulitply each side by 3.
Simplify.
Answer: The height of the ramp is about meters,

16. Answer: The roller coaster car was about 285 feet above the ground.
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.