If a right triangle has a hypotenuse that is twice the

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

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.

I couldn't solve this PS question. Can any expert give me some help? I would be thankful. <i class="em em---1"></i>

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Source: Beat The GMAT — Problem Solving | Fri Mar 16, 2018 4:22 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

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-xâˆš2, and a 30-60-90 triangle has side lengths x-xâˆš3-2x. 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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Mar 16, 2018 5:16 am

The sides of a 30-60-90 triangle are in the following ratio:
x : xâˆš3 : 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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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 : xâˆš3 : 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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