Question

A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.

Answer 1

`Slanted\ Roof = 20.77\ ft`

Explanation:

The question has missing attachment (See attachment 1 for complete figure)

Given

Width, W = 20ft

Let the taller height be represented with H and the shorter height with h

H = 10ft

h = 8ft

Overhang = 8 inch

Required

Determine the length of the slanted roof

FIrst, we have to determine the distance between the tip of the roof and the shorter height;

Represent this with

This is calculated by

`D = H - h`

Substitute 10 for H and 8 for h

`D = 10 - 8`

`D = 2ft`

Next, is to calculate the length of the slant height before the overhang;

See Attachment 2

Distance L can be calculated using Pythagoras theorem

`L^2 = 2^2 + 20^2`

`L^2 = 4 + 400`

`L^2 = 404`

Take Square root of both sides

`√(L^2) = √(404)`

`L = √(404)`

`L = 20.0997512422`

`L = 20.10\ ft` -------Approximated

The full length of the slanted roof is the sum of L (calculated above) and the overhang

`Slanted\ Roof = L + 8\ inch`

Substitute 20.10 ft for L

`Slanted\ Roof = 20.10\ ft + 8\ inch`

Convert inch to feet to get the slanted roof in feet

`Slanted\ Roof = 20.1\ ft + 8/12\ ft`

`Slanted\ Roof = 20.10\ ft + 0.67\ ft`

`Slanted\ Roof = 20.77\ ft`

Hence, the total length of the slanted roof in feet is approximately 20.77 feet