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Grade 10 · Trigonometry
Trigonometry: SOH-CAH-TOA, Sides and Angles
MEMORANDUM
Name:
Class:
Date:
Mark
/ 21
Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.
- 1Find x opposite a 30° angle, hypotenuse 8. (sine)(2)x = 8 sin 30° = 8 × 0,5 = 4✓✓ (2)
- 2Find x opposite a 50° angle, hypotenuse 10. (sine)(2)10 sin 50° ≈ 7,66✓✓ (2)
- 3Find x adjacent to a 60° angle, hypotenuse 14. (cosine)(2)14 cos 60° = 14 × 0,5 = 7✓✓ (2)
- 4Find x opposite a 40° angle, adjacent 9. (tangent)(2)9 tan 40° ≈ 7,55✓✓ (2)
- 5The side opposite a 30° angle is 5. Find the hypotenuse. (hypotenuse)(2)h = 5/(sin 30°) = 10✓✓ (2)
- 6opposite = 6, hypotenuse = 12. Find θ. (angle)(2)sinθ = 0,5 → θ = 30°✓✓ (2)
- 7adjacent = 8, hypotenuse = 16. Find θ. (angle)(2)cosθ = 0,5 → θ = 60°✓✓ (2)
- 8opposite = 5, adjacent = 5. Find θ. (angle)(2)tanθ = 1 → θ = 45°✓✓ (2)
- 9Give the exact value of sin 30° and tan 45°. (special)(2)1/2 and 1✓✓ (2)
- 10A rope to the top of a 6 m pole makes 40° with the ground. Rope length? (application)(3)sin 40° = 6/L → L = 6/(sin 40°) ≈ 9,33 m✓✓✓ (3)
TOTAL: 21 marks