Question

The acute angles of a right triangle are in ratio 2 : 3 . Find the difference of the angles.

Answer 1

Since its a right angled triangle then one of the angles must be ${90}^o$.

The sum of the angles in a triangle is ${180}^o$

Sum of acute angles in this triangle is ${180}^o-{90}^o={90}^o$

Let the first one be equal to $2x$ and the second on be $32$. The sum of $2x$ and $3x$ is ${90}^o$.

$2x+3x={90}^o$

$(2+3)x={90}^o$

$5x={90}^o$

$x=\frac{90}{5}$

$x={18}^o$.