Geometry and TrigonometryHardUsing tangent to find a side
Geometry and Trigonometry practice question
In a right triangle, one acute angle θ satisfies tan θ = 3/4. The leg adjacent to θ has length 12. What is the length of the leg opposite θ?
Answer: 9
Tangent is opposite over adjacent, so opposite/12 = 3/4. Multiply: opposite = 12 × 3/4 = 9. (The triangle is a scaled 3-4-5, with hypotenuse 15.)
Common wrong answers
- If you answered 15
- 15 is the hypotenuse of this triangle, not the opposite leg. The question asks for the leg opposite θ.
- If you answered 16
- 16 is 12 × 4/3, using the ratio upside down. tan θ = opposite/adjacent, so opposite = adjacent × tan θ = 12 × 3/4.
- If you answered 36
- 36 is 12 × 3, forgetting to divide by 4. The tangent is 3/4, not 3.
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