Answer:
23.094 ft approximately
(If you want your answer in a different format, let me know please.)
Step-by-step explanation:
I would have solve this using tangent since the side opposite to x is asked for and the adjacent side to side is given as having a measurement of 40 ft.
But I think they want you to use the formula:
.
![l=\frac{40}{\cos(30)}](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B40%7D%7B%5Ccos%2830%29%7D)
Input into calculator:
(approximation)
l represents the length of the roof.
So we have l=46.188 and b=40.
We must use the Pythagorean Theorem to find the height,h, for of the roof.
l is the hypotenuse.
![h^2+40^2=46.188^2](https://tex.z-dn.net/?f=h%5E2%2B40%5E2%3D46.188%5E2)
![h^2+1600=2133.331](https://tex.z-dn.net/?f=h%5E2%2B1600%3D2133.331)
Subtract 1600 on both sides:
![h^2=533.331](https://tex.z-dn.net/?f=h%5E2%3D533.331)
Take square root of both sides:
![h=23.094](https://tex.z-dn.net/?f=h%3D23.094)
The answer is 23.094 feet for the height that roof reaches on the building.
I want to show you another way:
![\tan(x)=\frac{\text{opposite}}{\text{adjacent}}](https://tex.z-dn.net/?f=%5Ctan%28x%29%3D%5Cfrac%7B%5Ctext%7Bopposite%7D%7D%7B%5Ctext%7Badjacent%7D%7D)
![\tan(30)=\frac{h}{40}](https://tex.z-dn.net/?f=%5Ctan%2830%29%3D%5Cfrac%7Bh%7D%7B40%7D)
Multiply both sides by 40:
![40\tan(30)=h](https://tex.z-dn.net/?f=40%5Ctan%2830%29%3Dh)
Input into calculator:
![23.094=h](https://tex.z-dn.net/?f=23.094%3Dh)
I didn't do it this way because your problem suggested you use their formula to find the height.