Chapter 12.6, Problem 9WE

To determine

To find the indicated part of triangle ABC.

Answer to Problem 9WE

  $A={13.8}^{\circ }$

Explanation of Solution

Given information :

  

Here we shall use the cosine formula.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Now we have to find smallest angle.

Smallest angle is always apposite to the smallest side.

Hence we find the angle opposite to smallest side.

Hence we put the values given,

  $\begin{array}{l}\cos A=\frac{{30}^2+{40}^2-{13}^2}{2\left(30\right)\left(40\right)}\\ \cos A=\frac{2331}{2400}\\ A={\cos }^{-1}-0.97125\\ A={13.8}^{\circ }\end{array}$