Question

Technology required. Ramps in a parking garage need to beboth steep and safe. The maximum safe incline for a ramp is8.5 degrees. Is this ramp safe? If not, provide dimensions thatwould make the ramp safe.

Answer 1

Ok, so:

Let me draw the situation here below:

Ok, let's find the angle first:

For this, we shall make use of the trigonometric functions:

In this case, the most useful function which could help us to solve this problem is tan(x). This function relations the opposite side of the angle and its adjacent side, like this:

tan(x) = opposite side / adjacent side

So, if we replace the values:

tan(x) = 15/95

tan(x) = 0,15789474

To find x, we could use the inverse function of tan(x). This one is called arctan(x).

So, arctan(tan(x)) = arctan(0,15789474)

And this is:

x = 8.97 degrees

Now, we can affirm that the angle is 8.97 degrees, which is bigger than 8.5 degrees.

Now, what should be the length of the bottom for the ramp to be safe?

Let me draw the situation:

We know that the ramp is safe if the maximum safe incline is 8.5°. So, what should be the value of x for this occurs?

We use the trigonometric function tan(x) again.

tan(8.5°) = 15/x

Remember that tan(8.5°) is a number

Then, x = 15/tan(8.5°), and this is 100.36

So, we conclude that the lenght of the bottom should be at least, 100.36