Geometry and TrigonometryVery hardSine from tangent
Geometry and Trigonometry practice question
In right triangle ABC, angle C is the right angle and tan A = 2. What is the value of sin A?
- A. 2√5/5Correct
- B. √5/5
- C. 1/2
- D. √5/2
Answer: A. 2√5/5
tan A = opposite/adjacent = 2, so take opposite = 2 and adjacent = 1. The hypotenuse is √(2² + 1²) = √5. Then sin A = opposite/hypotenuse = 2/√5 = 2√5/5.
Why the other answers are wrong
- B. √5/5
- √5/5 = 1/√5 is cos A (adjacent/hypotenuse), not sin A.
- C. 1/2
- 1/2 is adjacent/opposite, which is tan B (or 1/tan A), not a sine.
- D. √5/2
- √5/2 is hypotenuse/opposite — the ratio for sin A turned upside down.
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