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zysi [14]
3 years ago
13

(20 pts!) if the base of the roof has length 40 feet and x=30, which of the following gives the height of the roof?

Mathematics
2 answers:
musickatia [10]3 years ago
8 0

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{b}{\cos(x)}.

l=\frac{40}{\cos(30)}

Input into calculator:

l=46.188 (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

h^2+1600=2133.331

Subtract 1600 on both sides:

h^2=533.331

Take square root of both sides:

h=23.094

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}}

\tan(30)=\frac{h}{40}

Multiply both sides by 40:

40\tan(30)=h

Input into calculator:

23.094=h

I didn't do it this way because your problem suggested you use their formula to find the height.

artcher [175]3 years ago
6 0

Answer:

40/√3 feet

Step-by-step explanation:

Given,

Base of the roof,b=40 feet

Base angle,x=30°

Formula to calculate length of the roof,l=

\frac{b}{ \cos(x) }

or,l=40/cos(30°)

or,l=40*(√3/2)

or,l=80/√3

Now,In the above triangle, using Pythagoras formula,

hypotenuse^2=base^2+height^2

If total height be h,

h^2+b^2=l^2

or,h^2=l^2-b^2

or,h^2=(80/√3)^2-40^2

or,h^2=6400/3 - 1600

or,h^2=1600/3

or,h=40/√3

ANS:40/√3 feet

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