Pythagoras' Theorem and Trigonometry Quiz
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5 questions, one answer each
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1. A right-angled triangle has sides of length 5 cm and 12 cm. What is the length of the hypotenuse?
- A. 13 cm
- B. 17 cm
- C. 7 cm
- D. 14.4 cm
2. In a right-angled triangle, the angle is 30° and the hypotenuse is 10 cm. Using exact trigonometric values, what is the length of the side opposite to the 30° angle?
- A. 5√3 cm
- B. 5 cm
- C. 10√3 cm
- D. 5√2 cm
3. A cuboid has dimensions 3 cm, 4 cm and 12 cm. What is the length of the space diagonal (from one corner to the opposite corner)?
- A. 13 cm
- B. 15 cm
- C. 19 cm
- D. √169 cm
4. A non-right-angled triangle has sides a = 7 cm, b = 9 cm and angle C = 50°. Using the formula ½ab sin C, what is the area of the triangle?
- A. 31.5 sin(50°) cm²
- B. Approximately 24.1 cm²
- C. 32 cm²
- D. 63 sin(50°) cm²
5. In triangle ABC, angle A = 65°, angle B = 50°, and side a = 8 cm (opposite angle A). Using the sine rule, which expression correctly finds side b (opposite angle B)?
- A. b = 8 sin(65°)/sin(50°)
- B. b = 8 sin(50°)/sin(65°)
- C. b = 8 sin(65°) × sin(50°)
- D. b = sin(50°)/(8 sin(65°))