To find the required length of a ramp based on a height and an angle, you can use trigonometry. Specifically, you can use the sine function, which relates the angle of the ramp to the height and the length of the ramp.
Given:
- Height (opposite side) = 5 ft
- Angle (θ) = 4.8 degrees
The sine function is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the hypotenuse corresponds to the ramp length (L). Rearranging the formula to find the hypotenuse gives us:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the values, we get:
\[ L = \frac{5}{\sin(4.8^\circ)} \]
Now, you can calculate \(\sin(4.8^\circ)\) using a calculator:
\[ \sin(4.8^\circ) \approx 0.0832 \]
Now substituting this value back in:
\[ L = \frac{5}{0.0832} \approx 60.1 \]
Therefore, the length of the ramp needed, rounded to the nearest hundredth, is:
\[ \boxed{60.10 \text{ ft}} \]
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