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Chapter 9 Right Triangles and Trigonometry

SOLVE RIGHT TRIANGLES. USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS. Chapter 9 Right Triangles and Trigonometry. Section 9.6 Solving Right Triangles. SOLVE RIGHT TRIANGLES. Solving Right Triangles. C ONCEPT. S UMMARY. C. a. b. a. B. c.

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Chapter 9 Right Triangles and Trigonometry

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

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

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

  4. 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. 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

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

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

  8. 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

  9. 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

  10. 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

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

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

  13. Divide both sides by tan 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. Simplify. Answer: The audience member is about 60 feet from the base of the platform.

  14. 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

  15. Y W 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.

  16. 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? USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS Answer: The roller coaster car was about 285 feet above the ground.

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