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)

Answer 1

To find the length of the ramp, we can use the relationship between the angle of elevation, the height, and the length of the ramp, which forms a right triangle. In this scenario, we have:

- The height of the ramp (opposite side) = 5.3 feet
- The angle of elevation (θ) = 17°

We can use the sine function, which is defined as:

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

Let \( L \) be the length of the ramp (hypotenuse). Then the equation can be written as:

\[
\sin(17°) = \frac{5.3}{L}
\]

Rearranging this gives:

\[
L = \frac{5.3}{\sin(17°)}
\]

Now we need to calculate \( \sin(17°) \):

\[
\sin(17°) \approx 0.2924
\]

Now substitute this value back into the equation for \( L \):

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

So, to the nearest tenth, the length of the ramp is approximately **18.1 feet**.