Question

In a right angle triangle, two acute angles are in the ratio, $2:3$. Find the angles.

Answer 1

By angle sum property, $\angle A+\angle B+\angle C={180}^{\circ }$

Let the $△ABC$ be right angled at $A$

$\therefore \angle A={90}^{\circ }$

$\therefore \angle B+\angle C={180}^{\circ }-\angle A={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

Given that $\angle B:\angle C=2:3$

Let $\angle B=2x$ and $\angle C=3x$

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

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

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

$\therefore \angle B=2\times {18}^{\circ }={36}^{\circ }$ and $\angle C=3\times {18}^{\circ }={54}^{\circ }$

Hence the other two acute angles are ${36}^{\circ }$ and ${54}^{\circ }$