Question

For a ramp with an angle of elevation of 14 degrees and a height of 2.5 feet, how long is the distance of the ramp? Round your answer to the nearest whole number. In order to earn full credit show all your work including your original equation and steps to solve. You may use the button to upload a picture of your work.

Answer 1

To find the distance of the ramp (the length of the ramp), we can use trigonometry. We have the height of the ramp (the vertical side) and the angle of elevation.

First, let's define the problem using a right triangle:

- The height of the ramp (opposite side) = 2.5 feet
- The angle of elevation (θ) = 14 degrees
- The distance of the ramp (hypotenuse) = L

We can use the sine function because it relates the opposite side to the hypotenuse in a right triangle:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Substituting the known values into the equation gives:

\[
\sin(14^\circ) = \frac{2.5}{L}
\]

Next, we can rearrange this equation to solve for L (the length of the ramp):

\[
L = \frac{2.5}{\sin(14^\circ)}
\]

Now, we need to calculate \(\sin(14^\circ)\). Using a calculator:

\[
\sin(14^\circ) \approx 0.2419
\]

Now we can substitute \(\sin(14^\circ)\) back into the equation for L:

\[
L = \frac{2.5}{0.2419}
\]

Calculating this gives:

\[
L \approx 10.35 \text{ feet}
\]

Finally, rounding to the nearest whole number, we find:

\[
L \approx 10 \text{ feet}
\]

So, the length of the ramp is approximately **10 feet**.