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
and a height of 5.3 feet. To the nearest tenth, how long is the ramp?(1 point)
feet
Answers
GPT-4o mini
To find the length of the ramp, we can use the sine function from trigonometry. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
Here, the height of the ramp (the opposite side) is 5.3 feet and the angle of elevation is 17°. We want to find the length of the ramp, which is the hypotenuse (let's call it \( L \)).
The sine function gives us the following relationship:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \Rightarrow \sin(17^\circ) = \frac{5.3}{L}
\]
Now we can rearrange this equation to solve for \( L \):
\[
L = \frac{5.3}{\sin(17^\circ)}
\]
Now, we need to calculate \( \sin(17^\circ) \):
\[
\sin(17^\circ) \approx 0.2924
\]
Now we substitute this value into the equation:
\[
L = \frac{5.3}{0.2924} \approx 18.1 \text{ feet}
\]
So the length of the ramp is approximately **18.1 feet**.
Here, the height of the ramp (the opposite side) is 5.3 feet and the angle of elevation is 17°. We want to find the length of the ramp, which is the hypotenuse (let's call it \( L \)).
The sine function gives us the following relationship:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \Rightarrow \sin(17^\circ) = \frac{5.3}{L}
\]
Now we can rearrange this equation to solve for \( L \):
\[
L = \frac{5.3}{\sin(17^\circ)}
\]
Now, we need to calculate \( \sin(17^\circ) \):
\[
\sin(17^\circ) \approx 0.2924
\]
Now we substitute this value into the equation:
\[
L = \frac{5.3}{0.2924} \approx 18.1 \text{ feet}
\]
So the length of the ramp is approximately **18.1 feet**.