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:
[tex]l=\frac{b}{\cos(x)}[/tex].
[tex]l=\frac{40}{\cos(30)}[/tex]
Input into calculator:
[tex]l=46.188[/tex] (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.
[tex]h^2+40^2=46.188^2[/tex]
[tex]h^2+1600=2133.331[/tex]
Subtract 1600 on both sides:
[tex]h^2=533.331[/tex]
Take square root of both sides:
[tex]h=23.094[/tex]
The answer is 23.094 feet for the height that roof reaches on the building.
I want to show you another way:
[tex]\tan(x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
[tex]\tan(30)=\frac{h}{40}[/tex]
Multiply both sides by 40:
[tex]40\tan(30)=h[/tex]
Input into calculator:
[tex]23.094=h[/tex]
I didn't do it this way because your problem suggested you use their formula to find the height.
