Question

Ramps in a parking garage need to be steep. The maximum safe incline for a ramp is 8.5 degrees. Is this ramp safe? If not, provide dimensions that would make the ramp safe. 15 1 95 I Submit

Answer 1

a) The ramp is unsafe as the incline angle is more than the maximum safe incline

b) A measure of 14 by 95 is safe for the ramp

Here, we want to check if the ramp is safe

To do this, we shall calculate the angle between the hypotenuse of the triagle and the adjacent

From what we have in the diagram, we can see that the sides we have are the opposite and the adjacent

The appropriate trigonometric identity to use between the two is the tangent

The tangent of an angle is the ratio of the opposite to the adjacent

Let us call the angle theta

Thus;

`\begin{gathered} \tan \text{ }\theta\text{ = }(15)/(95) \\ \\ \theta\text{ = }\tan ^(-1)((15)/(95)) \\ \theta\text{ = 8.97 degre}es \end{gathered}`

This is more than the maximum angle of incline (8.5) and thus we can conclude that the ramp is not safe

To have the safe ramp, we can have a change to the dimensions

Let us have the angle as 8.5 without changing the horizintal distance. We have the value of the height of the ramp as follows;

`\begin{gathered} \tan \text{ 8.5 = }(h)/(95) \\ h\text{ = 95 tan 8.5} \\ h\text{ = 14.19 } \end{gathered}`

If the height is reduced to 14, then we can have a safe incline angle

Thus a measurement of height 14 and base 95 for the ramp will be a safe measure