Question

To get from the ship to the dock, Mae must walk up a ramp with an angle of elevation of 17°
and a height of 5.3 feet.
To the nearest tenth, how long is the ramp? (1 point)
feet

Answer 1

To find the length of the ramp, we can use trigonometric relationships. The height of the ramp and the angle of elevation form a right triangle, where the height of the ramp is the opposite side, the length of the ramp is the hypotenuse, and we can use the sine function.

The sine function is defined as:

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

In this case:

- \(\theta = 17^\circ\) (the angle of elevation)
- The opposite side (height of the ramp) = 5.3 feet.
- The hypotenuse (length of the ramp) = \(L\).

Therefore, we can set up the equation:

\[
\sin(17^\circ) = \frac{5.3}{L}
\]

We can rearrange the formula to solve for \(L\):

\[
L = \frac{5.3}{\sin(17^\circ)}
\]

Now we can calculate \(\sin(17^\circ)\):

\(\sin(17^\circ) \approx 0.2924\) (using a calculator).

Now substitute this value into the equation:

\[
L = \frac{5.3}{0.2924} \approx 18.1 \text{ feet}
\]

Thus, the length of the ramp, to the nearest tenth, is approximately:

\[
\boxed{18.1 \text{ feet}}
\]