Chapter 10.6, Problem 12P

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

$\cos T$

To determine

To find the value of the expression.

Answer to Problem 12P

The value of $\cos T$ is equals to $0.724$ .

Explanation of Solution

Given information:

The given expression is $\cos T$

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 angle T.

  $\begin{array}{l}\frac{RS}{\sin T}=\frac{RT}{\sin S}\\ \frac{20}{\sin T}=\frac{29}{1}\left[\sin S=\sin 90=1\right]\\ \sin T\cdot 29=20\left[\text{cross multiplication}\right]\\ \sin T=\frac{20}{29}\left[\text{divide each side by 29}\right]\\ T={\sin }^{-1}\left(\frac{20}{29}\right)\end{array}$

Substitute the value of angle T in the expression

  $\begin{array}{l}\cos T=\tan {\sin }^{-1}\left(\frac{20}{29}\right)\\ =0.724\left[\text{use calculator}\right]\end{array}$

The value of $\cos T$ is equals to $0.724$ .