The roof shown in the diagram above is shown from the front of the house. The slope of the roof is 5/12 The height of the roof is 15 feet. What is the length from gutter to peak of the roof?

Step-by-step explanation:cj4ygifbiybruonfceggr3e

A^2 = B^2 + C^

Step-by-step explanation:

Use the Pythagorean theorem to find the missing side of a right triangle.

A^2 = B^2 + C^2

corson

corson

Member

member

Jan 29, 2011

#3

A. Use this equation to model the roof and solve for the distance of the horizontal leg of the right triangle. y is the height (15) and m is your slope (5/12). b is 0 because on the coordinate plane we are using, the line is not shifted from the origin.

Code:

y = mx + b

So we substitute.

Code:

15 = (5/12)x + 0

15*(12/5) = x

36 = x

Now we use the pythagorean theorem a^2 + b^2 = h^2 where a and b are the legs and h is the hypotenuse.

Code:

15^2 + 36^2 = h^2

1521 = h^2

sqrt(1521) = h

39 = h

39 ft should be the length of one side of the roof if I'm thinking straight.

Jan 29, 2011

#4

Use the Pythagorean theorem to find the missing side of a right triangle.

A^2 = B^2 + C^2

^ would be failing at the Pythagorean theorem (not to offend)

To solve this problem:

First off, a straight line is 180°, there is one 90° angle on one side of line, meaning that the angle adjacent to it is supplementary (or equaling 180° when added together) the supplement of 90° is 90°. So the angle adjacent to the right angle is also a right angle. Meaning that we are now dealing the 2 right triangles. To make this problem more easy to work with, we are going to assign each of the vertices a variable; starting at the "Peak" and going clockwise we are going to start with A, B, C, then D (This is going around the whole bid triangle, not one of the smaller ones)

Slope is measured in rise over run, or, in this problem, 5/12