You must use sinθ=
![\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20)
first to identify AC,
sin45=
![\frac{AC}{24}](https://tex.z-dn.net/?f=%20%5Cfrac%7BAC%7D%7B24%7D%20)
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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
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}](https://tex.z-dn.net/?f=%20a%5E%7B2%7D%20)
+
![b^{2}](https://tex.z-dn.net/?f=%20b%5E%7B2%7D%20)
=
![c^{2}](https://tex.z-dn.net/?f=%20c%5E%7B2%7D%20)
![(AC)^{2}](https://tex.z-dn.net/?f=%20%28AC%29%5E%7B2%7D%20)
+
![(BC)^{2}](https://tex.z-dn.net/?f=%20%28BC%29%5E%7B2%7D%20)
=
![AB^{2}](https://tex.z-dn.net/?f=%20AB%5E%7B2%7D%20)
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}](https://tex.z-dn.net/?f=%20%2816.97%29%5E%7B2%7D%20)
+
![BC^{2}](https://tex.z-dn.net/?f=%20BC%5E%7B2%7D%20)
=
![(24)^{2}](https://tex.z-dn.net/?f=%20%2824%29%5E%7B2%7D%20)
Moving
![(16.97)^{2}](https://tex.z-dn.net/?f=%20%2816.97%29%5E%7B2%7D%20)
to right,,
![BC^{2}](https://tex.z-dn.net/?f=%20BC%5E%7B2%7D%20)
=
![(24)^{2}](https://tex.z-dn.net/?f=%20%2824%29%5E%7B2%7D%20)
-
![(16.97)^{2}](https://tex.z-dn.net/?f=%20%2816.97%29%5E%7B2%7D%20)
![BC^{2}](https://tex.z-dn.net/?f=%20BC%5E%7B2%7D%20)
= 576-288
![BC^{2}](https://tex.z-dn.net/?f=%20BC%5E%7B2%7D%20)
= 288
![\sqrt{BC}](https://tex.z-dn.net/?f=%20%5Csqrt%7BBC%7D%20)
=
![\sqrt{288}](https://tex.z-dn.net/?f=%20%5Csqrt%7B288%7D%20)
( 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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
× base × height
![\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
× 16.97 ×16.97
To get 96 square feet.