Question

In a right angled triangle one of the acute angle is twice the othe. prove that hypotenause is double the shorter side

Answer 1

in right angled∆
one angle is 90°
let acute angle=x
second acute angle=2x
sum of all angles of right angled ∆ is 180°
so , 90°+x°+2x°=180°
3x=90
x=30
so, second acute angle is 60°
so , 30°-60°-90° triangle theorem
side opposite to30°
(side opposite to30° ) =hypotenuse ×1/2
so, hypotenuse = 2×(side opposite to30° )
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