Question

Find the area please

Answer 1

Answer:

D

Step-by-step explanation:

Recall that the area of a triangle is given by:

$\displaystyle A = \frac{1}{2} bh$

In this case, the base is x and the height is y. Hence:

$\displaystyle A = \frac{1}{2} xy$

We can write the following ratios:

$\displaystyle \sin \alpha = \frac{x}{12} \text{ and } \cos \alpha = \frac{y}{12}$

Solve for x and y:

$\displaystyle x = 12\sin \alpha \text{ and } y = 12\cos \alpha$

Substitute:

$\displaystyle A = \frac{1}{2}\left(12\sin \alpha\right)\left(12\cos \alpha\right)$

And simplify. Hence:

$\displaystyle A = 72\sin \alpha \cos\alpha$

In conclusion, our answer is D.