Chapter 12, Problem 1CR

To determine

To find: The measure of the larger acute angle of a right angled triangle.

Answer to Problem 1CR

The measure of the larger acute angle is ${81}^{\text{o}}.$

Explanation of Solution

Given Information:

  $y=9\times x$

Where $x\text{and}y$ are the two acute angles

Formula used:

Sum of all internal angles of a triangle $={180}^{\text{o}}$

Calculation:

Let $x\text{and}y$ be the larger and smaller acute angles respectively.

As the given triangle is a right triangle

So, the measure of an angle other than $x\text{and}y$ will be ${90}^{\text{o}}$

We know that,

Sum of all internal angles of a triangle $={180}^{\text{o}}$

  $\therefore x+y+{90}^{\text{o}}={180}^{\text{o}}$

As $y=9x$ … (Given)

  $\begin{array}{l}\therefore x+9x+{90}^{\text{o}}={180}^{\text{o}}\\ \therefore 10x={180}^{\text{o}}-{90}^{\text{o}}\\ \therefore 10x={90}^{\text{o}}\\ \therefore x=9^{\text{o}}\\ \therefore y=9\times 9^{\text{o}}\\ \therefore y={81}^{\text{o}}\end{array}$

Hence, the measure of the larger acute angle is ${81}^{\text{o}}.$