Chapter 10.6, Problem 9P

For $\Delta JKLand\Delta RST$, find the value of each expression.

$\sin R$

To determine

To find the value of the expression.

Answer to Problem 9P

The value of $\sin R$ is equals to $\frac{21}{29}$ .

Explanation of Solution

Given information:

The given expression is $\sin R$

The lengths of the sides are given as $RT=29,TS=21\text{ and SR}=20$

Formula used:

Law of sines.

In any triangle, the ratio of side length to the sine of its opposite angle is the same for all three sides.

Calculation :

Use law of sines to evaluate the expression .

  $\begin{array}{l}\frac{TS}{\sin R}=\frac{RT}{\sin S}\\ \frac{21}{\sin R}=\frac{29}{1}\left[\sin S=\sin 90=1\right]\\ \sin R\cdot 29=21\left[\text{cross multiplication}\right]\\ \sin R=\frac{21}{29}\left[\text{divide each side by 29}\right]\end{array}$

The value of $\sin R$ is equals to $\frac{21}{29}$ .