Geometry and TrigonometryHardSide from a cosine value and the hypotenuse
Geometry and Trigonometry practice question
In triangle ABC, angle C is a right angle, cos A = 0.8, and AB = 15. What is the length of BC?
Answer: 9
cos A = AC/AB = 0.8, so sin A = 0.6 (since sin² + cos² = 1). BC is opposite A: BC = AB × sin A = 15 × 0.6 = 9.
Common wrong answers
- If you answered 12
- 12 is AC, the side adjacent to A (15 × 0.8).
- If you answered 18.75
- 18.75 comes from 15 ÷ 0.8.
- If you answered 0.6
- 0.6 is sin A, not a length.
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