Chapter 13.5, Problem 35HP

To determine

To find: The measure of the largest angle.

Answer to Problem 35HP

Measure of largest angle is ${102}^0$

Explanation of Solution

Given information:

  $\begin{array}{l}a=8\\ b=14.5\\ c=10.6\end{array}$

Using law of cosines

We get

  $b^2=a^2+c^2-2ac\cos B$

On substituting values

We get

  $\begin{array}{l}{b}^2=a^2+c^2-2ac\cos B\\ \Rightarrow {\left(14.5\right)}^2=8^2+{10.6}^2-2\left(8\right)\left(10.6\right)\cos B\\ \Rightarrow 210.25=64+112.36-169.6\cos B\\ \Rightarrow 210.25=176.36-169.6\cos B\\ \Rightarrow 169.6\cos B=176.36-210.25\\ \Rightarrow 169.6\cos B=-33.89\\ \Rightarrow \cos B=\frac{-33.89}{169.6}\\ \Rightarrow \cos B=-0.2\\ \Rightarrow B={\cos }^{-1}\left(-0.2\right)\\ \Rightarrow B={102}^0\end{array}$

The longest side is $14.5$ centimeters.

On using law of cosines we got the angle that is opposite to the longest side.

Therefore,

Measure of largest angle is ${102}^0$