Question
to get from the ship to the dock, mae must walk up a ramp with an angle of elevation of 17 degrees and a height of 5.3 feet. to the nearest tenth, how long is the ramp
Answers
GPT-4o mini
To find the length of the ramp, we can use trigonometry, specifically the sine function. The sine of an angle in a right triangle is defined as the ratio of the opposite side (height in this case) to the hypotenuse (length of the ramp).
Given:
- Height (opposite side) = 5.3 feet
- Angle of elevation = 17 degrees
Using the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Substituting the values:
\[
\sin(17^\circ) = \frac{5.3}{L}
\]
where \( L \) is the length of the ramp. Rearranging the equation to solve for \( L \):
\[
L = \frac{5.3}{\sin(17^\circ)}
\]
Next, we need to calculate \( \sin(17^\circ) \):
\[
\sin(17^\circ) \approx 0.2924
\]
Now plug this value into the equation to find \( L \):
\[
L = \frac{5.3}{0.2924} \approx 18.1
\]
Therefore, the length of the ramp, to the nearest tenth, is approximately:
\[
\boxed{18.1} \text{ feet}
\]
Given:
- Height (opposite side) = 5.3 feet
- Angle of elevation = 17 degrees
Using the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Substituting the values:
\[
\sin(17^\circ) = \frac{5.3}{L}
\]
where \( L \) is the length of the ramp. Rearranging the equation to solve for \( L \):
\[
L = \frac{5.3}{\sin(17^\circ)}
\]
Next, we need to calculate \( \sin(17^\circ) \):
\[
\sin(17^\circ) \approx 0.2924
\]
Now plug this value into the equation to find \( L \):
\[
L = \frac{5.3}{0.2924} \approx 18.1
\]
Therefore, the length of the ramp, to the nearest tenth, is approximately:
\[
\boxed{18.1} \text{ feet}
\]