Question

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

Answer 1

sum of all angles in a triangle $={180}^{\circ }$

sum of acute angle $={90}^{\circ }$

$\Rightarrow 2x+3x={90}^{\circ }$

$\Rightarrow 5x={90}^{\circ }$

$\Rightarrow x=\frac{{90}^{\circ }}{5}={18}^{\circ }$

The angles are $2x=2\times 18={36}^{\circ }$ and $3x=3\times {18}^{\circ }={54}^{\circ }$