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2 of 212 of 21 Items 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?(2 points) feet Skip to navigation page 1 of 1

Answer 1

To find the length of the ramp, we can use the sine function from trigonometry. We know the height of the ramp (opposite side) and the angle of elevation. The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

Let \( L \) be the length of the ramp (the hypotenuse). The sine function gives us:

\[
\sin(θ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}
\]

Where:
- \( θ = 17° \)
- \( h = 5.3 \) feet

Rearranging the equation to solve for \( L \):

\[
L = \frac{h}{\sin(θ)} = \frac{5.3}{\sin(17°)}
\]

Now, we can calculate \( \sin(17°) \). Using a calculator:

\[
\sin(17°) \approx 0.2924
\]

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

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

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