Question
To get from the ship to the dock, Mae must walk up a ramp with an angle of elevation of 18 ° and a height of 6.3 feet. To the nearest tenth, how long is the the ramp?
Answers
GPT-4o mini
To find the length of the ramp that Mae must walk, we can use the relationship defined by the sine function in a right triangle. In this case, we know the opposite side (the height of the ramp) and we want to find the hypotenuse (the length of the ramp).
The relevant trigonometric function is:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Where:
- \(\theta\) is the angle of elevation (18°)
- The opposite side is the height of the ramp (6.3 feet)
- The hypotenuse is the length of the ramp (let's call it \(L\))
Rearranging the sine function to solve for \(L\):
\[
L = \frac{\text{opposite}}{\sin(\theta)} = \frac{6.3}{\sin(18°)}
\]
Now, we need to calculate \(\sin(18°)\):
\(\sin(18°) \approx 0.3090\)
Now substitute this value into the formula for \(L\):
\[
L = \frac{6.3}{0.3090} \approx 20.3 \text{ feet}
\]
Therefore, the length of the ramp, to the nearest tenth of a foot, is approximately:
\[
\boxed{20.3 \text{ feet}}
\]
The relevant trigonometric function is:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Where:
- \(\theta\) is the angle of elevation (18°)
- The opposite side is the height of the ramp (6.3 feet)
- The hypotenuse is the length of the ramp (let's call it \(L\))
Rearranging the sine function to solve for \(L\):
\[
L = \frac{\text{opposite}}{\sin(\theta)} = \frac{6.3}{\sin(18°)}
\]
Now, we need to calculate \(\sin(18°)\):
\(\sin(18°) \approx 0.3090\)
Now substitute this value into the formula for \(L\):
\[
L = \frac{6.3}{0.3090} \approx 20.3 \text{ feet}
\]
Therefore, the length of the ramp, to the nearest tenth of a foot, is approximately:
\[
\boxed{20.3 \text{ feet}}
\]