Question

The acute angles of a right triangle are in the ratio $4:5$ Find the measure of these angles.

Answer 1

We have a right angled triangle , in which one angle is 90° and other two are given in the ratio $4:5$

Other angles$=4:5=4x:5x$ (where $x$ is some constant ) .

We know that , Sum of all interior angles of triangle is $180°$.

$$\begin{gathered} \Rightarrow {90}^{\circ }+4x+5x={180}^{\circ } \\ \Rightarrow 9x={180}^{\circ }-{90}^{\circ } \\ \Rightarrow 9x={90}^{\circ } \\ \Rightarrow x=\frac{{90}^{\circ }}{9}=10 \\ \Rightarrow x=10 \end{gathered}$$

Other angles = $$\begin{gathered} 4\times 10={40}^{\circ } \\ 5\times 10={50}^{\circ } \end{gathered}$$

Hence the required angles are $40°\mathrm{and}50°$