Question

In a right triangle , the hypotenuse is 2 times as long as its one side, then one of the acute angle is

Answer 1

solution :

one side of the triangle = x

hypotenuse of the triangle = 2x

so,using Pythagoras theorem....

base^2+alt^2 = hyp^2

x^2+alt^2 = (2x)^2 [2x^2 =2^2*x^2]

alt^2 = 4x^2-x^2

alt^2 = 3x^2

alt = √3x^2 [√x^2 = x]

alt = √3x

We know the ratio = 30° : 60° : 90°

= 1 : √3 : 2

so the acute angle are 30° and 60°