The pitch of a roof is given as a single digit, such as 7 pitch. This actually means this roof has a rise of 7 feet for every 12 feet of horizontal run. What is the angle of a roof with a pitch of 7? Round to the nearest 0.10. Group of answer choices 35.7 degrees 0.6 degrees 30.3 degrees 88.1 degrees
The correct answer and explanation is:
The pitch of a roof is often expressed as a ratio of the vertical rise to the horizontal run. In your example, a 7 pitch means the roof rises 7 feet vertically for every 12 feet horizontally.
To find the angle of the roof relative to the horizontal, we use basic trigonometry. The pitch essentially forms a right triangle where:
- The rise (opposite side) = 7 feet
- The run (adjacent side) = 12 feet
- The angle θ is between the run (horizontal) and the hypotenuse (roof slope)
Step 1: Use the tangent function
The tangent of the angle is the ratio of the opposite side to the adjacent side: tan(θ)=riserun=712\tan(\theta) = \frac{\text{rise}}{\text{run}} = \frac{7}{12}
Step 2: Calculate the angle using arctangent (inverse tangent)
θ=arctan(712)\theta = \arctan\left(\frac{7}{12}\right)
Using a calculator: θ=arctan(0.5833)≈30.255∘\theta = \arctan(0.5833) \approx 30.255^\circ
Step 3: Round to the nearest 0.10 degree
θ≈30.3∘\theta \approx 30.3^\circ
Final answer:
The angle of the roof with a 7 pitch is approximately 30.3 degrees.
Explanation in detail:
Roof pitch is a convenient way to describe the steepness of a roof without directly stating the angle. The standard “pitch” uses a run of 12 feet, which means every roof pitch number describes how many feet the roof rises over a 12-foot horizontal distance.
To convert pitch to an angle, the tangent function is perfect because it relates the angle of a right triangle to the ratio of its opposite and adjacent sides.
- Tangent = rise / run
- Angle = arctangent(rise / run)
This allows anyone to quickly figure out the slope’s angle in degrees, which is useful for understanding how steep the roof actually is, for construction, safety, or architectural purposes.
Among the options you provided:
- 35.7 degrees is close but too high for a 7/12 pitch
- 0.6 degrees is far too small
- 30.3 degrees matches our calculation
- 88.1 degrees is almost vertical, not reasonable here
Thus, 30.3 degrees is the correct answer.