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.