Chapter 6.6, Problem 26E

To determine

To find: The indicated quantity of the triangle.

Answer to Problem 26E

The indicated quantity of the triangle is $126.53°$

Explanation of Solution

Given information:

The given figure of the triangle is,

Concept used:

Law of Sines:

If ABC is a triangle with sides $a$ , $b$ , and $c$ , then

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

The angle $\theta$ of the triangle is calculated as,

  $\begin{array}{l}\frac{a}{\sin A}=\frac{c}{\sin C}\\ \frac{10}{\sin \theta }=\frac{8}{\sin 40°}\\ \theta =126.53°\end{array}$

Therefore, the indicated quantity of the triangle is $126.53°$ .