Chapter 8, Problem 23CR

To determine

To find : the value of y^o

Answer to Problem 23CR

The value of y is 23⁰

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 y^ois as follows.

  

  $\begin{array}{c}{4}^2={10}^2+{10}^2-2\left(10\right)\left(10\right)\cos y°\\ 16=200-200\cos y°\\ 1-\cos y°=\frac{16}{200}\end{array}$

  $\begin{array}{c}\cos y°=1-\frac{16}{200}\\ =0.92\\ y=23.07°\\ \simeq 23°\end{array}$