4.12.2 Solving Right Triangles
- 1. Solving Right Triangles The student is able to (I can): • Find the missing parts of a right triangle • Use trig ratios to solve problems
- 2. To “solve” a right triangle means to find all of the missing parts of the right triangle. If you are given an angle and a side: • Subtract the angle from 90° to find the other acute angle • Use trig ratios to find one of the missing sides • Use either trig ratios or Pythagorean Theorem to find the third side
- 3. If you are given two sides: • Use Pythagorean Theorem to find the missing side • Use trig ratios to find an angle – Unless all of your sides work out to be whole numbers, be sure to use the two given sides in your trig ratio to prevent rounding errors. • Subtract the angle you found from 90° to find the other angle
- 4. Examples Solve the triangles. Round sides to the nearest tenth and angles to the nearest whole degree. 1. m∠D=_____ ED = ______ BD = ______ 6 67°B E D tan67 6 6tan67 14.1 ED ED ° = = ° ≈ m 90 67 23D∠ = − = °
- 5. Examples Solve the triangles. Round sides to the nearest tenth and angles to the nearest whole degree. 1. m∠D=_____ ED = ______ BD = ______ 6 67°B E D adj opp hyp tan67 6 6tan67 14.1 ED ED ° = = ° ≈ m 90 67 23D∠ = − = ° 23° 14.1
- 6. Examples Solve the triangles. Round sides to the nearest tenth and angles to the nearest whole degree. 1. m∠D=_____ ED = ______ BD = ______ 6 67°B E D adj opp hyp tan67 6 6tan67 14.1 ED ED ° = = ° ≈ m 90 67 23D∠ = − = ° 2 2 2 6 14.1 234.81 15.3 BD BD = + = ≈ 23° 14.1 15.3
- 7. 2. TA = _____ m∠A = _____ m∠T = _____ 12 18 T A M
- 8. 2. TA = _____ m∠A = _____ m∠T = _____ It doesn’t matter whether you use ∠T or ∠A. The triangle is labeled for ∠T. 12 18 T A M2 2 2 18 12 468 21.6 TA TA = + = ≈ hyp opp adj 21.6
- 9. 2. TA = _____ m∠A = _____ m∠T = _____ It doesn’t matter whether you use ∠T or ∠A. The triangle is labeled for ∠T. 12 18 T A M2 2 2 18 12 468 21.6 TA TA = + = ≈ hyp opp adj 1 12 tan 18 12 tan 18 34 T T − = = ≈ ° 90 34 56 m A∠ = − = ° 21.6 56° 34°