Question

Find the measure of each angle.

The measures of the acute angles of a right triangle are in the ratio$5:7$.

Short answer

The measures of each angle is${90}^{\circ },37\cdot 5^{\circ }$ and$52\cdot 5^{\circ }$ .

Step-by-step solution

Step 1. Given information.

The ratio between acute angles of a right triangle is,

$5:7$

Step 2. Concept used.

The sum of angles of a triangle is${180}^{\circ }$.

And, one angle of a right triangle is${90}^{\circ }$${90}^{\circ }$.

Since, ratio of the angles is always in the simplified form,

It might not represent the actual measure.

Step 3. Considering the angles as5x and7x .

The sum of the angles of the triangle can be expressed using the above relation as,

$\begin{array}{c}5x+7x=90\\ 12x=90\\ x=7.5\end{array}$

So, each of the angles are given by,

$\begin{array}{c}5x=5\times 7\cdot 5\\ 5x=37.5\end{array}$

And,

$\begin{array}{c}7x=7\times 7\cdot 5\\ 7x=52.5\end{array}$

Therefore, the angles of right triangle are${90}^{\circ },37\cdot 5^{\circ }$ and $52\cdot 5^{\circ }$.