Chapter 9, Problem 2SAP

To determine

To find: correct option that represents the area of $\Delta ABC$ .

Answer to Problem 2SAP

B.

Explanation of Solution

Given information:

The figure of $\Delta ABC$ is shown below.

  

The options are as follows:

10 $\sin x$

40 $\sin x$

80 $\sin x$

40 $\cos x$

80 $\cos x$

Calculation:

Redraw the triangle as shown below.

  

The area of $\Delta ABC$ will be as follows:

  $\begin{array}{c}\text{Area of }\Delta ABC=\frac{1}{2}\left(AD\right)\left(BD\right)\\ =\frac{1}{2}\left(AD\right)\left(AB\sin x\right)\left(\because \frac{BD}{AB}=\sin x\right)\\ =\frac{1}{2}\left(10\right)\left(8\sin x\right)\left(\text{Put }AD=10\text{ and }AB=8\right)\\ =40\sin x\end{array}$

The area of triangle is $40\sin x$ . So, option B. is correct.