To determine if the stairs meet safety regulations, we first need to calculate the angle of inclination using the rise and run of the stairs.
The angle of inclination \( \theta \) can be calculated using the tangent function:
\[ \tan(\theta) = \frac{\text{rise}}{\text{run}} \]
Given that the rise is 6 inches and the run is 9 inches:
\[ \tan(\theta) = \frac{6}{9} = \frac{2}{3} \]
To find \( \theta \), take the arctan of both sides:
\[ \theta = \arctan\left(\frac{2}{3}\right) \]
Using a calculator, we find that \( \theta \approx 33.69^\circ \).
Since the angle of inclination is approximately 33.69 degrees, which falls within the range of 30 to 35 degrees specified by the building safety code, these stairs meet safety regulations.
a set of stairs has a rise of 6 inches and run of 9 inches the building safety code says that stairs should rise at an angle of between 30 degrees and 35 degrees does this set of stairs meet safety regulations justify your answer by showing mathematical proof
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