Chapter 8.6, Problem 62STP

To determine

To determine the area of the given triangle.

Answer to Problem 62STP

Option C is correct.

Explanation of Solution

Given information :

$\sin x=0.6$ and $AB=12$

We know that $\sin x=\frac{\text{Opposite}}{\text{Hypotenuse}}=0.6$

As AB=12

We get,

$\begin{array}{l}\frac{BC}{AB}=0.6\\ \frac{BC}{12}=0.6\\ BC=7.2\end{array}$

Now using Pythagoras theorem we get,

$CA=\sqrt{{12}^2-{7.2}^2}=9.6$

Area is $\frac{1}{2}\left(7.2\right)\left(9.6\right)=34.6$ units²

Option C is correct.