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If a right triangle has a hypotenuse that is twice the length
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28 Apr 2017, 23:00
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
(A) 15 degrees
(B) 22.5 degrees
(C) 30 degrees
(D) 45 degrees
(E) 60 degrees
Re: If a right triangle has a hypotenuse that is twice the length
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28 Apr 2017, 23:11
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)
(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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If a right triangle has a hypotenuse that is twice the length
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28 Apr 2017, 23:32
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
(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.
