Question

Find the area please

Answer 1

D

Explanation:

Recall that the area of a triangle is given by:

`\displaystyle A = (1)/(2) bh`

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

`\displaystyle A = (1)/(2) xy`

We can write the following ratios:

`\displaystyle \sin \alpha = (x)/(12) \text{ and } \cos \alpha = (y)/(12)`

Solve for x and y:

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

Substitute:

`\displaystyle A = (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.