Question

The maximum slope of a wheelchair ramp is 1:12. For a wheelchair ramp made with these specifications, What angle does the ramp make with the ground? Round your answer to the nearest hundredth.
1) 6.91 degrees
2) 5.39 degrees
3) 8.24 degrees
4) 4.76 degrees

Answer 1

Answer:

The answer is 4) 4.76 degrees.

Step-by-step explanation:

The slope of the ramp is 1:12, which means for every 1 unit of vertical rise, there are 12 units of horizontal run.

We can use the tangent of the angle to find the angle of the ramp. The tangent of an angle in a right triangle is the ratio of the opposite side (rise) to the adjacent side (run).

So, tan(0) = 1/12

To find the angle, we use the inverse tangent function, also known as arctan or tan^-1.

0 = tan^-1 (1/12)

This will give us the angle in radians. To convert to degrees, we multiply by 180/π

0 = tan^-1 (1/12) × 180/π

This gives us the angle of the ramp to the nearest hundredth of a degree.

0 = 4.76 degrees. So, the correct answer is 4) 4.76 degrees.

Answer 2

Answer:

4) 4.76 degrees

Step-by-step explanation:

The maximum slope of a wheelchair ramp is given as 1:12. This ratio indicates that for every 12 units of horizontal distance (ground length), the ramp rises by 1 unit.

The formula to calculate the angle (θ) in degrees when given the slope ratio (rise:run) is:

$\sf Tan(\theta) = \dfrac{\textsf{rise}}{\textsf{run}}$

In terms of $\theta$:

$\sf \theta = \arctan\left(\dfrac{\textsf{rise}}{\textsf{run}}\right)$

In this case, the rise is 1, and the run is 12.

Substituting these values into the formula:

$\sf \theta = \arctan\left(\dfrac{1}{12}\right)$

Now, calculate the angle:

$\sf \theta \approx \arctan(0.08333333333)$

$\sf \theta \approx 4.763641691^\circ$

$\sf \theta \approx 4.76^\circ \textsf{ (in 2 d.p.)}$

Therefore, the correct answer is option 4) 4.76 degrees.