Geometry and TrigonometryMediumTrigonometric ratios (SOH-CAH-TOA)
Geometry and Trigonometry practice question
In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length 5. What is sin θ?
- A. 3/5Correct
- B. 4/5
- C. 3/4
- D. 5/3
Answer: A. 3/5
sin θ = opposite / hypotenuse = 3/5 (the 'SOH' in SOH-CAH-TOA). Choice B (4/5) would be cos θ, using the adjacent side of 4.
Why the other answers are wrong
- B. 4/5
- 4/5 is cos θ — that's the adjacent side (found from 5² − 3²) over the hypotenuse. Sine uses the opposite side: 3/5.
- C. 3/4
- 3/4 is opposite over adjacent, which is tan θ. Sine puts the opposite side over the hypotenuse: 3/5.
- D. 5/3
- You flipped the ratio — 5/3 is hypotenuse over opposite. SOH means opposite on top: 3/5.
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