Question

The legs of a right triangle are lengths x and x√3. The cosine of the smallest angle of the triangle is _____.
A 1/2
B √3
C (√3)/2
D 2√3

Answer 1

The smallest angle of the triangle is the angle opposite the shortest leg of the triangle, which in this case is x.

Answer 2

So

Answer 3

Now h = sqr(x^2 + x(sqr3)^2)
= sqr(x^2 + 3x^2)
= sqr(4x^2)
= 2x

Answer 4

The cosine of an angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse, so in this case the cosine of the required angle = x(sqr3)/2x. This simplified will give the answer.

Answer 5

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Answer 6

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