Chapter 12.6, Problem 15WE

To determine

To determine the angles of the triangle formed.

Answer to Problem 15WE

  $\begin{array}{l}A={51.14}^{\circ }\\ B={69.13}^{\circ }\\ C={59.73}^{\circ }\end{array}$

Explanation of Solution

Given information :

  

First we shall find the sides of the triangle.

  

In the diagram above we found out all the sides of the triangle using the length of the radius.

Now,

AB= 61 in

BC= 55 in

CA=66 in

Now we shall find the angles of the triangle.

Use cosine law to determine the angles.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Put values we get,

  $\begin{array}{l}\cos A=\frac{{61}^2+{66}^2-{55}^2}{2\left(61\right)\left(66\right)}\\ A={51.14}^{\circ }\\ \cos B=\frac{{61}^2+{55}^2-{66}^2}{2\left(61\right)\left(55\right)}\\ B={69.13}^{\circ }\\ \cos C=\frac{{66}^2+{55}^2-{61}^2}{2\left(66\right)\left(55\right)}\\ C={59.73}^{\circ }\end{array}$