Question

GEOMETRY-PLEASE HELP ME ILL GIVE 20 POINTS

Answer 1

You must use sinθ=
`(opposite)/(hypotenuse)` first to identify AC,
sin45=
`(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
`(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

`√(BC)` =
`√(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,

`(1)/(2)` × base × height

`(1)/(2)` × 16.97 ×16.97
To get 96 square feet.