The roof is to have a 5-12 pitch. If the eaves of the roof are 10 feet off the ground, and the eave to eave width of the house is 36 feet, what is the total height of the roof at its highest point?

17.5 feet

Step-by-step explanation:

since the roof has a 5-12 pitch, this means that the roof rises by 5 units for every 12 unit run.

Height of eaves off the ground is 10 feet

If the eave to eave width of the house is 36 feet, then the distance of one eaves to the center will be 36/2 = 18 feet

since the pitch is 5-12, then the height of the highest point of the  roof from the eave will be  gotten from the relationship below

=

where y is the height of the highest point of the  roof from the eaves

5 x 18 = 12y

90 = 12y

y = 90/12 = 7.5 feet

total height of roof at highest point will be height of the eaves off the ground plus height of highest point of the roof from the eaves

total height of roof = 10 + 7.5 = 17.5 feet