Using Pitch in Right Triangle Calculations
Using Pitch to Solve Right Triangle Lengths
In construction problems, we sometimes are working with roots and other structures that are shaped as right triangles. In roofing applications, we are often working with the pitch of the roof. The pitch is similar to the standard angle of right triangle.
The pitch is defined in 1 unit of rise over 12 units of run. In the United States, the units are typically either feet or yards.
pitch = 1 unit of rise / 12 units of run
With the right triangle, we can use similar triangles to determine that:
pitch /12 = rise / run
Knowing either one of the variables, we can use ratio calculations to determine the other.
Example 1:
Pitch: 3/12, Run: 48
Rise:
12/48 = 3/x
x = 3 * 48 / 12
x = 12
Hypotenuse:
√(48^2 + 12^2) ≈ 49.4773
Example 2:
Pitch: 5/12, Rise: 30
Run:
5/12 = 30/x
x = 30 * 12 / 5
x = 72
Hypotenuse:
√(30^2 + 72^2) = 78
Approximating Angle with Pitch
To find the angle using pitch:
θ = atan(pitch / 12)
If you do not have a scientific calculator, you can approximate the angle by using any of the approximations (these are not the only approximation equations). They were found using the curve fitting features of a Casio fx-9860gii.
θ ≈ 3.72674504 * p + 2.78886014 (r^2 = 0.99084258)
θ ≈ 4.93070418 * p^0.91971679 (r^2 = 0.997149)
θ ≈ -0.1158911 * p^2 + 5.17538414 * p - 0.3498579 (r^2 = 0.9999772)
Data used: θ to four decimal places are used.
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Using Pitch to Solve Right Triangle Lengths
In construction problems, we sometimes are working with roots and other structures that are shaped as right triangles. In roofing applications, we are often working with the pitch of the roof. The pitch is similar to the standard angle of right triangle.
The pitch is defined in 1 unit of rise over 12 units of run. In the United States, the units are typically either feet or yards.
pitch = 1 unit of rise / 12 units of run
With the right triangle, we can use similar triangles to determine that:
pitch /12 = rise / run
Knowing either one of the variables, we can use ratio calculations to determine the other.
Example 1:
Pitch: 3/12, Run: 48
Rise:
12/48 = 3/x
x = 3 * 48 / 12
x = 12
Hypotenuse:
√(48^2 + 12^2) ≈ 49.4773
Example 2:
Pitch: 5/12, Rise: 30
Run:
5/12 = 30/x
x = 30 * 12 / 5
x = 72
Hypotenuse:
√(30^2 + 72^2) = 78
Approximating Angle with Pitch
To find the angle using pitch:
θ = atan(pitch / 12)
If you do not have a scientific calculator, you can approximate the angle by using any of the approximations (these are not the only approximation equations). They were found using the curve fitting features of a Casio fx-9860gii.
θ ≈ 3.72674504 * p + 2.78886014 (r^2 = 0.99084258)
θ ≈ 4.93070418 * p^0.91971679 (r^2 = 0.997149)
θ ≈ -0.1158911 * p^2 + 5.17538414 * p - 0.3498579 (r^2 = 0.9999772)
Data used: θ to four decimal places are used.
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.