University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2022
Views:

17

Pages:

6
Author:

SpaceCadet101

Pre-Calculus Right Triangle Trigonometry Review Name: Key Convert from Radians to Degrees, or Degrees to Radians 1. 40° * (π/180°) = 2π/9 2. 190° * (π/180°) = 19π/18 3. 145° * (π/180°) = 29π/36 4. (7π/6) * (180°/π) = 210° 5. (11π/4) * (180°/π) = 495° Find the six trig functions of θ. 6. sinθ = 3/5 cscθ = 5/3 cosθ = 4/5 secθ = 5/4 tanθ = 3/4 cotθ = 4/3 7. sinθ = 3/4 cscθ = 4/3 cosθ = √7/4 secθ = 4/√7 = 4√7/7 tanθ = 3/√7 = 3√7/7 cotθ = √7/3 Find the exact value for x. 8. cos45° = x/9 √2/2 = x/9 x = 9√2/2 9. sin60° = 14/x √3/2 = 14/x √3x = 28 x = 28√3/3 Evaluate without using a calculator. 10. (sin45°)² + (cos45°)² (√2/2)² + (√2/2)² 1/2 + 1/2 = 1 11. (tan60°)² + (csc45°)² (√3)² + (√2)² 3 + 2 = 5 12. sin(π/4) + cos(π/4) √2/2 + √2/2 = √2 Solve the triangle. Find all missing sides and angles, as exact values. 13. x = 4√6 y = 4√6 * √2 = 8√3 14. x = 3√3 * √2 = 3√6 y = 3√3 Find the value of x and/or y. Find an exact answer for x in #15 and #17 15. 24² + x² = 30² x = 18 16. sin60° = y/32 y = 32 * √3/2 = 16√3 sin48° = x/36.95 x ≈ 36.95 17. x = 60 * √3/2 = 30√3 y = 30√3 + 30√3/3 = 40√3 Determine the measurements for angle θ for each of the following triangles. Round to the nearest tenth of a degree. 18. sinθ = 12/13 θ = sin⁻¹(12/13) ≈ 67.4° 19. cosθ = 6/11 θ = cos⁻¹(6/11) ≈ 56.9° 20. tanθ = 15/8 θ = tan⁻¹(15/8) ≈ 61.9° Applications: Draw a picture for each! Round all answers to the nearest tenth. 21. An airplane is at an elevation of 35,000 ft when it begins its approach to an airport. Its angle of descent is 6°. a) What is the distance between the airport and the point on the ground directly below the airplane? tan(84°) = x/35,000 x = 333,002.8 ft b) What is the approximate air distance between the plane and the airport? cos(84°) = 35,000/y y = 334,837.0 ft 22. Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long. tan(A) = 16/9 A = 60.6° B = 29.4° 23. Find the measures of the angles of an isosceles triangle whose sides are 5, 10, and 10. cos(θ) = 2.5/10 θ = 75.5° Base angles congruent! 75.5°, 75.5°, 29° 24. An engineer builds a 75-foot vertical cellular phone tower. Find the angle of elevation to the top of the tower from a point on level ground 95 feet from its base. tan(θ) = 75/95 θ = 38.3° 25. A skateboard ramp touches the ground at one point, and is 4 ft off the ground at its highest point. The angle of elevation the ramp makes with the ground is 18.4°. What is the length of the ramp? sin(18.4°) = 4/x x ≈ 12.7 ft 26. An escalator 152 feet in length rises to a platform and makes a 30° angle with the ground. Find the height of the platform above the ground. sin(30°) = h/152 h = 76 ft 27. Points A and B (on the same side of a tower) are 12 m apart. The angles of elevation of the top of a tower are 35° and 45° respectively. Find the tower's height. tan(45°) = h/x h = x*tan(45°) tan(35°) = h/(x+12) h = (x+12)*tan(35°) x*tan(45°) = (x+12)*tan(35°) x = 8.4 h = 8.4

Math Triangle Trigonometry Review Solution

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