Question

In a right triangle the two acute angles are in the ratio $7:11$. Find the measure of acute angles.

Answer 1

According to the problem:

Sum of angles of a triangle $={180}^{\circ }$

Let us consider the acute angles $=11x$ and $7x$

Implies that

${180}^{\circ }-{90}^{\circ }=11x+7x$

Implies that

$90=11x+7x$

Implies that

$90=18x$

$x=\frac{90}{18}$

Implies that

$x=5$

Hence the acute angle is

$7\times 5={35}^{\circ }$

and

$11\times 5={55}^{\circ }$