Geometry and Trigonometry practice question

Answer: C. 12

In a 30-60-90 triangle the sides are in ratio 1 : √3 : 2, with the hypotenuse twice the shorter leg. So hypotenuse = 2(6) = 12. Choice B (6√3) is the longer leg, and choice A (6√2) is the 45-45-90 pattern.

Why the other answers are wrong

A. 6√2

6√2 comes from the 45-45-90 ratio 1 : 1 : √2. This is a 30-60-90 triangle, ratio 1 : √3 : 2, so the hypotenuse is 2(6) = 12.

B. 6√3

6√3 is the longer leg (opposite the 60° angle). The hypotenuse is the shorter leg times 2, so 12.

D. 18

You multiplied the shorter leg by 3 instead of by 2 — the 3 in this triangle appears as √3 for the longer leg, while the hypotenuse is 2(6) = 12.

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