Chapter 8, Problem 23CT

To determine

To find : the value of x^o

Answer to Problem 23CT

The value of x is 32⁰

Explanation of Solution

Given information: An isosceles triangle with three given sides and unknown angle in Figure.

Formula used:

  

For any triangle, we can use law of cosines to relate three sides and one of the angles as, $c^2=a^2+b^2-2ab\cos C^0$

Calculation:

The law of cosines can be applied in the given triangle to calculate angle x^ois as follows.

  

  $\begin{array}{c}{20}^2={20}^2+{34}^2-2\left(20\right)\left(34\right)\cos x°\\ 34=40\cos x°\\ \cos x°=\frac{34}{40}\\ x=31.78°\\ \simeq 32°\end{array}$