ACT Math · Triangles and similarity
In a 30-60-90 triangle, the hypotenuse has length 14. Which value is closest to the length of the longer leg?
In a 30-60-90 triangle, the hypotenuse has length 14. Which value is closest to the length of the longer leg?
Answer and explanation
Answer: B: 12.1
In a -- triangle, the side lengths are in the ratio , with the hypotenuse the longest. The hypotenuse is , so the shorter leg is and the longer leg is , choice B. Check with the Pythagorean theorem: . Choice A () is the shorter leg. Choice C () is , from a -- ratio. Choice D () is the hypotenuse, which is always longer than either leg.
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