Chapter 12.1, Problem 24E

To determine

To find: the measurement of acute angle in the right triangle.

Answer to Problem 24E

  ${10}^0{\text{ and 80}}^0$ .

Explanation of Solution

Given:

The measurement of one acute angle is $8$ time the measurement of another acute angle.

Concept used:

Triangular sum theory:

The acute angles of right triangle are complementary.

Sum of the three angles of triangle is always ${180}^0$ .

If the triangle is right triangle then other two angles other than ${90}^0$ will be less than ${90}^0$ .

Calculation:

The measure of one acute angle is $8$ times the measure of the other acute angle.

Assuming $m\angle 1=x^0\text{ and }m\angle 2=8x^0$ .

According to the triangular sum theory:

The acute angles of right triangle are complementary.

Sum of two acute in angles right triangle is:

  $\begin{array}{l}{\left(8x\right)}^0+{\left(x\right)}^0=90.\\ 9x=90.\\ x=10.\end{array}$

So, the two acute angles are:

  $\begin{array}{l}8x=8\left(10\right)={80}^0.\\ {10}^0.\end{array}$

Hence, ${10}^0{\text{ and 80}}^0$ .