Geometry and TrigonometryMediumAdjacent leg from a sine value
Geometry and Trigonometry practice question
In a right triangle, one acute angle θ satisfies sin θ = 0.28, and the hypotenuse has length 25. What is the length of the leg adjacent to θ?
Answer: 24
cos θ = √(1 − 0.28²) = √(1 − 0.0784) = 0.96. The adjacent leg is 25 × 0.96 = 24. (It is a 7-24-25 triangle.)
Common wrong answers
- If you answered 7
- 7 is the leg opposite θ (25 × 0.28).
- If you answered 18
- 18 is 25 − 7, subtracting instead of using cosine.
- If you answered 0.96
- 0.96 is cos θ, not a length.
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