Chapter 12.5, Problem 17WE

To determine

Find the measure of angle $\left(\angle AOB\right)$ of triangle AOB such that radius of circle having centre $\left(O\right)$ , is 13 cm and length $\left(AB\right)$ is 10 cm.

  

Answer to Problem 17WE

The measure of angle $\angle AOB$ is $45.2°$ .

Explanation of Solution

Given information: It is given that the radius of circle whose centre $\left(O\right)$ is 13 cm and length $\left(AB\right)$ is 10 cm as shown.

  

Calculation: If $\angle AOB=\left(\theta \right)$ then by law of cosines in triangle AOB,

  $\begin{array}{c}\cos \left(\theta \right)=\frac{{\left(13\right)}^2+{\left(13\right)}^2-{\left(10\right)}^2}{2\left(13\right)\left(13\right)}\\ \cos \left(\theta \right)=\frac{119}{169}\\ \theta ={\cos }^{-1}\left(\frac{119}{169}\right)\\ \theta =45.2°\end{array}$

Hence angle $\angle AOB$ is $45.2°$ .