Chapter 12.1, Problem 22E

To determine

To find: the measurement of acute angles.

Answer to Problem 22E

The acute angles are ${34}^0,{56}^0$ .

Explanation of Solution

Given:

  

Concept used:

If the triangle is right triangle then sum of the other two angles is ${90}^0$ .

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:

If the triangle is right triangle then sum of the other two angles is ${90}^0$ .

  $\begin{array}{l}{\left(19x-1\right)}^0+{\left(13x-5\right)}^0={90}^0.\\ 32x-6={90}^0.\\ 32x=96.\\ x=3.\end{array}$

So, the two acute angles are:

  $\begin{array}{l}{\left(19x-1\right)}^0={\left(19\left(3\right)-1\right)}^0={56}^0.\\ {\left(13x-5\right)}^0\\ ={\left(13\left(3\right)-5\right)}^0.\\ {34}^0.\end{array}$

Hence, the acuteanglesare ${34}^0,{56}^0$ .