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# If a right triangle has a hypotenuse that is twice the length

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Current Student
Joined: 28 May 2014
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If a right triangle has a hypotenuse that is twice the length  [#permalink]

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28 Apr 2017, 23:00
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72% (00:53) correct 28% (01:11) wrong based on 73 sessions

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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

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Re: If a right triangle has a hypotenuse that is twice the length  [#permalink]

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28 Apr 2017, 23:11
According to pythogoras theorem
(2x)^2 = x^2 + a^2
This is because, from the given information, we can deduce the hypotnuse to be 2x provided the smaller side is x
a^2 = 3x^2 or a = x*sqrt(3)
If the sides are in ratio 1:sqrt(3):2, angles of the right triangle are 30,60,90
Smaller angle: 30(Option C)
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28 Apr 2017, 23:32
saswata4s 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

Sides of a 30-60-90 triangle are in the ratio $$1:\sqrt{3}:2$$
Let the smallest side be a, then the hypotenuse is 2a. The angle opposite a is the smallest angle and hence 30.

C.
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Re: If a right triangle has a hypotenuse that is twice the length  [#permalink]

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29 Apr 2017, 05:36
saswata4s 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

Cos X = 1/2
we know that all the angle are below 90 ..
So x = 60
smallest angle = 30
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Re: If a right triangle has a hypotenuse that is twice the length  [#permalink]

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19 Mar 2018, 16:20
saswata4s 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.

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Re: If a right triangle has a hypotenuse that is twice the length   [#permalink] 19 Mar 2018, 16:20
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