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

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

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

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

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  24.319

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

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

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 + 33.69 =90 mA  67.38  22.62

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)2 + 142 = 252 (XZ)2 + 196 = 225 (XZ)2 = 29

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 34.06 + mY = 90 mY  55.94 mX  34.06

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

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.

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.

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.

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 0.314 meters,

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.