Chapter 8.1, Problem 75AYU

Finding the Pitch of a Roof A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet. A steel support beam 46 feet in length is positioned in the center of the garage. To support the roof, another beam will be attached to the top of the center beam (see the figure). At what angle of elevation is the new beam? In other words, what is the pitch of the roof?

To determine

At what angle of elevation is the new beam? In other words, what is the pitch of the roof?

Answer to Problem 75AYU

The pitch of the roof is approximately $69°$.

Explanation of Solution

Given:

A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet. A steel support beam 46 feet in length is positioned in the center of the garage. To support the roof, another beam will be attached to the top of the center beam (see the figure).

Formula used:

$\text{tan}A=\frac{\text{opp side}}{\text{base}}$

Calculation:

Height above the wall $=46-20=26$ ft.

$\text{tan}A=\frac{26}{10}=2.6$

$A={\tan }^{-1}2.6$

$A\approx 69°$

The pitch of the roof is approximately $69°$.