The pitch of the roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8. What is its slope expressed as a positive number? What does the slope mean in this story?

Refer to the diagram shown below.

The height is h ft

Half of the total horizontal base length is w ft.

Because the pitch is 8, therefore

When w = 12 ft, then h = 8 ft.

That is

w/h = 12/8

w = 1.5h

The slope is h/w = 8/12 = 2/3.

As an angle,

θ = tan⁻¹ 2/3 = 33.7°

Answer:

Slope = 2/3.

The slope represents an angle of elevation of 33.7°.