University:
Concordia University Texas
Course:
MTH 3101 | Problem Solving: Algebra, Geometry, and Trigonometry
Academic year:

2019
Views:

190

Pages:

6
Author:

helkoktcj

Certainly, here's the breakdown of the image you provided: Title: Geometry Instructions: State if each triangle is acute, obtuse, or right. 1) 6 ft, 9 ft, 11 ft 6² + 9² = 117 11² = 121 117 < 121 Acute 2) 9 m, 14 m, 15 m 9² + 14² = 225 15² = 225 225 = 225 Right 3) 10 yd, 20 yd, 2√14 yd 10² + (2√14)² = 100 + 56 = 156 20² = 400 156 < 400 Obtuse 4) 11 cm, 146 cm, √146 cm 11² + (√146)² = 121 + 146 = 267 (√146)² = 146 267 > 146 Acute Find the missing side of each triangle. 5) 12² + 9² = x² 144 + 81 = x² x² = 225 x = 15 6) 7² + x² = 12² 49 + x² = 144 x² = 95 x = √95 Find the value of each trigonometric ratio. 7) tan A tan(A) = 3/4 8) cos C cos(C) = 4/5 9) tan Z tan(Z) = 15/8 10) sin X sin(X) = 3/5 Find the missing side lengths. Leave your answers as radicals in simplest form. 11) 30° - 60° - 90° triangle Short leg = 3 Hypotenuse = 6 Long leg = 3√3 12) 45° - 45° - 90° triangle Leg = 4 Hypotenuse = 4√2 Specific Problems: A 45-45-90 triangle is given. One leg is labeled as 5√2. The other leg is labeled as 5. The hypotenuse is labeled as 10. A 30-60-90 triangle is given. The hypotenuse is labeled as 7. The shorter leg is labeled as 3.5. The longer leg is labeled as 3.5√3. A 45-45-90 triangle is given. One leg is labeled as 5. The other leg is labeled as 5. The hypotenuse is labeled as 5√2. A 30-60-90 triangle is given. The hypotenuse is labeled as 9. The shorter leg is labeled as 4.5. The longer leg is labeled as 4.5√3. A 45-45-90 triangle is given. One leg is labeled as 6. The other leg is labeled as 6. The hypotenuse is labeled as 6√2. A 30-60-90 triangle is given. The hypotenuse is labeled as 15. The shorter leg is labeled as 7.5. The longer leg is labeled as 7.5√3. Find the missing side. Round to the nearest tenth. A right triangle is given. One angle is labeled as 70 degrees. The hypotenuse is labeled as 18. The side opposite the 70-degree angle is labeled as x. Solution: sin(70) = x/18, x = 18 * sin(70) ≈ 16.9 A right triangle is given. One angle is labeled as 42 degrees. The hypotenuse is labeled as 16. The side adjacent to the 42-degree angle is labeled as x. Solution: cos(42) = x/16, x = 16 * cos(42) ≈ 11.9 A right triangle is given. One angle is labeled as 35 degrees. The side opposite the 35-degree angle is labeled as 19. The side adjacent to the 35-degree angle is labeled as x. Solution: tan(35) = 19/x, x = 19 / tan(35) ≈ 27.2 A right triangle is given. One angle is labeled as 42 degrees. The hypotenuse is labeled as 21. The side adjacent to the 42-degree angle is labeled as x. Solution: cos(42) = x/21, x = 21 * cos(42) ≈ 15.6 Find the measure of the indicated angle to the nearest degree. A right triangle is given. The hypotenuse is labeled as 51. The side adjacent to the unknown angle is labeled as 28. Solution: cos(θ) = 28/51, θ = cos⁻¹(28/51) ≈ 57° A right triangle is given. The side opposite the unknown angle is labeled as 12. The side adjacent to the unknown angle is labeled as 37. Solution: tan(θ) = 12/37, θ = tan⁻¹(12/37) ≈ 18° A right triangle is given. The hypotenuse is labeled as 55.5. The side adjacent to the unknown angle is labeled as 29. Solution: cos(θ) = 29/55.5, θ = cos⁻¹(29/55.5) ≈ 58°