You must use sinθ= [tex] \frac{opposite}{hypotenuse} [/tex] first to identify AC,
sin45= [tex] \frac{AC}{24} [/tex]
By cross multiplying!,,,
sin45× 24 = AC
AC= 16.97056275 (Rounded= 16.97)
So, now you have base! But the triangle's formula is [tex] \frac{1}{2} [/tex] 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, [tex] a^{2} [/tex]+[tex] b^{2} [/tex]=[tex] c^{2} [/tex]
[tex] (AC)^{2} [/tex]+[tex] (BC)^{2} [/tex]= [tex] AB^{2} [/tex]
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,
[tex] (16.97)^{2} [/tex] +[tex] BC^{2} [/tex] = [tex] (24)^{2} [/tex]
Moving [tex] (16.97)^{2} [/tex] to right,,
[tex] BC^{2} [/tex] = [tex] (24)^{2} [/tex] - [tex] (16.97)^{2} [/tex]
[tex] BC^{2} [/tex] = 576-288
[tex] BC^{2} [/tex] = 288
[tex] \sqrt{BC} [/tex] = [tex] \sqrt{288} [/tex] ( 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,
[tex] \frac{1}{2} [/tex] × base × height
[tex] \frac{1}{2} [/tex] × 16.97 ×16.97
To get 96 square feet.
