Answer:
D
Step-by-step explanation:
Recall that the area of a triangle is given by:
[tex]\displaystyle A = \frac{1}{2} bh[/tex]
In this case, the base is x and the height is y. Hence:
[tex]\displaystyle A = \frac{1}{2} xy[/tex]
We can write the following ratios:
[tex]\displaystyle \sin \alpha = \frac{x}{12} \text{ and } \cos \alpha = \frac{y}{12}[/tex]
Solve for x and y:
[tex]\displaystyle x = 12\sin \alpha \text{ and } y = 12\cos \alpha[/tex]
Substitute:
[tex]\displaystyle A = \frac{1}{2}\left(12\sin \alpha\right)\left(12\cos \alpha\right)[/tex]
And simplify. Hence:
[tex]\displaystyle A = 72\sin \alpha \cos\alpha[/tex]
In conclusion, our answer is D.
