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 the sine function from trigonometry. In this scenario, we know the height of the ramp (the opposite side) and the angle of elevation. We can use the formula:

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

Where:
- \(\theta\) is the angle of elevation (17°),
- the opposite side is the height of the ramp (5.3 feet),
- and the hypotenuse is the length of the ramp (which we are trying to find).

Rearranging the formula to solve for the hypotenuse gives us:

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

Substituting in the known values:

\[
\text{hypotenuse} = \frac{5.3}{\sin(17°)}
\]

Now, we can calculate \(\sin(17°)\):

\[
\sin(17°) \approx 0.2924
\]

So we can find the length of the ramp:

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

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

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