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

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New post 28 Apr 2017, 23:00
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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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New post 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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New post 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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New post 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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New post 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.

Answer: C
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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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