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If a right triangle has a hypotenuse that is twice the

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by M7MBA » Fri Mar 16, 2018 4:22 am
If a right triangle has a hypotenuse that is twice the length of the shortest side, then what is the measure of the triangle's smallest angle?

(A) 15 degrees
(B) 22.5 degrees
(C) 30 degrees
(D) 45 degrees
(E) 60 degrees

The OA is the option C.

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by ErikaPrepScholar » Fri Mar 16, 2018 5:15 am
We can solve this problem quickly if we know our special triangles — a 45-45-90 triangle has side lengths x-x-x√2, and a 30-60-90 triangle has side lengths x-x√3-2x. From this, we know that if our hypotenuse is 2 times the length of our smallest side, we must have a 30-60-90 triangle, making the smallest angle 30 degrees.
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by GMATGuruNY » Fri Mar 16, 2018 5:16 am
The sides of a 30-60-90 triangle are in the following ratio:
x : x√3 : 2x
Since the hypotenuse = 2x and the shortest side = x, the hypotenuse is twice the shortest side.
No other right triangle has a hypotenuse that is twice the shortest side.
M7MBA wrote:If a right triangle has a hypotenuse that is twice the length of the shortest side, then what is the measure of the triangle's smallest angle?

(A) 15 degrees
(B) 22.5 degrees
(C) 30 degrees
(D) 45 degrees
(E) 60 degrees
Since the triangle must be a 30-60-90 triangle, the smallest angle = 30.

The correct answer is C.
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by Scott@TargetTestPrep » Mon Mar 19, 2018 3:33 pm
M7MBA wrote:If a right triangle has a hypotenuse that is twice the length of the shortest side, then what is the measure of the triangle's smallest angle?

(A) 15 degrees
(B) 22.5 degrees
(C) 30 degrees
(D) 45 degrees
(E) 60 degrees
We may recall that the side ratio of a 30-60-90 triangle = x : x√3 : 2x

We see that the hypotenuse is double the side opposite the 30-degree angle, so we have a 30-60-90 right triangle, with smallest angle of 30 degrees.

Answer: C

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