Geometry and TrigonometryMediumLeg from a tangent ratio and the hypotenuse
Geometry and Trigonometry practice question
In a right triangle, tan θ = 3/4 for one of the acute angles θ, and the hypotenuse has length 25. What is the length of the leg opposite θ?
Answer: 15
tan θ = 3/4 means the legs are in the ratio 3 : 4, a 3-4-5 triangle scaled by 5: legs 15 and 20, hypotenuse 25. The leg opposite θ is 15.
Common wrong answers
- If you answered 3
- 3 is the unscaled ratio value.
- If you answered 20
- 20 is the leg adjacent to θ.
- If you answered 18.75
- 18.75 is 25 × 3/4, treating tan as opposite over hypotenuse.
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