Question

GEOMETRY-PLEASE HELP ME ILL GIVE 20 POINTS

Answer 1

You must use sinθ= $\frac{opposite}{hypotenuse}$ first to identify AC,
sin45= $\frac{AC}{24}$
By cross multiplying!,,,
sin45× 24 = AC
AC= 16.97056275 (Rounded= 16.97)
So, now you have base! But the triangle's formula is $\frac{1}{2}$ base× height,,, So , you need height which is BC,
To find BC, 
You could use cos , tan or sin as well, but I find Pythagorean Theorem slightly easy, So I'll show you that ---
Which is, $a^{2}$+$b^{2}$=$c^{2}$
$(AC)^{2}$+$(BC)^{2}$= $AB^{2}$
So, we have AC= 16.97, and AB= 24
That's sufficient for what we want,  let's plug in our values into the formula,
$(16.97)^{2}$ +$BC^{2}$ = $(24)^{2}$
Moving $(16.97)^{2}$ to right,,
$BC^{2}$ = $(24)^{2}$ - $(16.97)^{2}$
$BC^{2}$ = 576-288
$BC^{2}$ = 288
$\sqrt{BC}$ = $\sqrt{288}$ ( squaring both sides )
BC = 16.97 ft.
So, now we have Base = 16.97 and height same= 16.97
And now you can find the area,
$\frac{1}{2}$ × base × height
$\frac{1}{2}$ × 16.97 ×16.97 
To get 96 square feet.