Question

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

Answer 1

In the right-angled triangle, one angle must be of $90°$.

Let the ratio be $x$.

So, the other angles are $2x,3x$.

We know that sum of the angles of a triangle is $180°$.

$$\begin{gathered} 2x+3x+90°=180° \\ 5x+90°=180° \\ 5x=180°-90° \\ 5x=90° \\ x=\frac{90°}{5}=18° \end{gathered}$$

Hence, the angles are $2x=2(18°)=36°$

And, the other angle $3x=3(18°)=54°$.