Chapter 14, Problem 13CPE

To determine

Tofind: the value of $\sin C$

Answer to Problem 13CPE

The value of $\sin C$ is $\frac{15}{17}$ .

Explanation of Solution

Given information:

In $\Delta ABC$ , $A\overline{B}\perp B\overline{C}$ , $AB=15\text{ and }BC=8$ .

Calculation: to find the value of $\sin C$ , draw the triangle,

Now, the value of $\sin C$ is,

$\begin{array}{l}\sin C=\frac{AB}{AC}\\ \sin C=\frac{15}{\sqrt{{\left(15\right)}^2+{\left(8\right)}^2}}\text{ [substitute and use of pythagoras formula]}\\ \sin C=\frac{15}{17}\text{ [simplify]}\end{array}$

Thus, The value of $\sin C$ is $\frac{15}{17}$ .