4.12.2 Solving Right Triangles
- 1. 4.12.2 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
- 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 ED tan67 6 ED 6tan67 14.1 ° = = ° ≈ m D 90 67 23∠ = − = ° 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 ED tan67 6 ED 6tan67 14.1 ° = = ° ≈ m D 90 67 23∠ = − = ° 2 2 2 BD 6 14.1 BD 234.81 15.3 = + = ≈ 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 TA 18 12 TA 468 21.6 = + = ≈ 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 TA 18 12 TA 468 21.6 = + = ≈ hyp opp adj 1 12 tanT 18 12 T tan 18 34 − = = ≈ ° m A 90 34 56 ∠ = − = ° 21.6 56° 34°