A set of stairs has a rise of 6 inches and a run of 9 inches. The building safety code says the stairs should rise at an angle of between 30 degrees and 35 degrees. Does this set of stairs meet the safety regulations? Justify your answer by showing mathematical proof.
compare 6/9 to tan35°
To determine if this set of stairs meets the safety regulations, we need to calculate the angle of inclination using the given rise and run values.
The formula for calculating the angle of inclination (θ) is:
θ = arctan(rise / run)
Given that the rise is 6 inches and the run is 9 inches, we can substitute these values into the formula:
θ = arctan(6 / 9)
To calculate this, we can use a calculator or a trigonometric table. In this case, the angle of inclination is approximately 33.69 degrees.
Since the calculated angle is within the range of 30 to 35 degrees, this set of stairs meets the safety regulations.
To determine if the set of stairs meets the safety regulations, we need to calculate the angle of the stairs using trigonometry.
The rise of the stairs is given as 6 inches, and the run is given as 9 inches. We can use the tangent function to find the angle of the stairs.
The formula to find the angle of a right triangle is:
tan(angle) = opposite / adjacent
In this case, the opposite side is the rise (6 inches) and the adjacent side is the run (9 inches). Let's plug these values into the formula:
tan(angle) = 6 / 9
To find the angle, we take the inverse tangent (also called arctangent) of both sides of the equation:
angle = arctan(6 / 9)
Using a calculator, we can find the arctangent of 6/9 to get the angle:
angle ≈ 33.69 degrees
The calculated angle is approximately 33.69 degrees.
Since the calculated angle of the stairs falls within the range of 30 degrees to 35 degrees specified by the building safety code, we can conclude that this set of stairs meets the safety regulations.