To find the length of the ramp, we can use the relationship between the height of the ramp, the angle of elevation, and the length of the ramp itself. The height of 5.3 feet represents the opposite side of the triangle, while the length of the ramp represents the hypotenuse.
We can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
\[ \sin(17^\circ) = \frac{5.3 \text{ feet}}{\text{hypotenuse}} \]
Let \( L \) be the length of the ramp (the hypotenuse). Rearranging the equation gives us:
\[ L = \frac{5.3 \text{ feet}}{\sin(17^\circ)} \]
Now we can calculate \( L \):
- First, calculate \( \sin(17^\circ) \). Using a calculator, we find:
\[ \sin(17^\circ) \approx 0.2924 \]
- Now, substitute this value back into the equation:
\[ L = \frac{5.3}{0.2924} \approx 18.1 \text{ feet} \]
Thus, the length of the ramp to the nearest tenth is:
\[ \boxed{18.1} \text{ feet} \]
1 answer