Geometry and TrigonometryVery hardSine from a tangent ratio
Geometry and Trigonometry practice question
In a right triangle, tan A = 8/15 for one of the acute angles A. What is the value of sin A? (Enter your answer as a fraction.)
Answer: 8/17
tan A = opposite/adjacent = 8/15 makes the hypotenuse √(64 + 225) = 17, so sin A = 8/17.
Common wrong answers
- If you answered 15/17
- 15/17 is cos A; sine puts the opposite side (8) on top.
- If you answered 8/15
- 8/15 is tan A itself; sine divides by the hypotenuse 17.
- If you answered 17/8
- The hypotenuse is the denominator of sine, not the numerator.
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