Geometry and Trigonometry practice question

Answer: A. 4√3

In a 30-60-90 triangle the sides are in the ratio 1 : √3 : 2, with the shortest side opposite the 30° angle. The short leg is 4, so the hypotenuse is 8 and the longer leg is 4√3. Check: 4² + (4√3)² = 16 + 48 = 64 = 8².

Why the other answers are wrong

B. 8

8 is the hypotenuse — twice the short leg. The question asks for the longer LEG, which is the short leg times √3.

C. 2√3

2√3 would be the longer leg if the short leg were 2. Here the short leg is 4, so the longer leg is 4√3.

D. 4

4 is the short leg itself, the side opposite 30°. The longer leg is √3 times that.

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