SOLUTION: A roof rises 9.75 ft over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundredth?

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Question 69841: A roof rises 9.75 ft over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundredth?
Found 2 solutions by tutorcecilia, bucky:
Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean Theorem to solve

Let a=9.75
Let b=17.24
Let c=the hypotenuse (the side opposite the right triangle.
.
[plug-in the values and solve for c]

[take the square root of each side to find the value of "c"]
.
c=19.806
.
check by plugging all of the values back into the original equation:

392.278=392.28

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
A roof rises 9.75 ft over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundredth?
Slope is defined as the amount the roof goes up (vertical) divided by the corresponding
distance that it goes horizontally.
Since the roof goes up 9.75 feet in 17.24 feet of horizontal distance the slope (call it
S) is:

Calculator time. Do the division to find the answer is 0.56554 which rounds to 0.57
to the nearest hundredth.
Architects generally do not identify the Slope of a roof this way. They express it in
terms of the pitch ... how many inches does the roof go up per inches of horizontal
run. For example, a "4 in 12" pitch means the roof goes up 4 inches for each 12 inches it
goes horizontally. To convert this slope to architect's pitch we could write:

where V is the vertical distance and 12 is the number of inches in a foot. By substituting
0.57 for S, the equation becomes:

Solve this by multiplying both sides by 12 to get:

So in this case the Architect would say the pitch of the roof is 6.84 in 12 meaning
that the roof rises 6.84 inches for each 12 inches of horizontal distance.
Recognize that this would drive a carpenter crazy. A carpenter would know how to build
a 6 in 12 pitched roof or a 7 in 12 pitched roof, but the mathematics of being a 6.84
in 12 pitched roof would drive most of them into fits of laughter. The architect
would generally specify a 7 in 12 pitch for this problem. But then mathematicians
never seem to worry about the practicality of their answers ... sigh ...
Sorry for
the "extra" information, but it's a slice of real life.