To find the length of the ramp needed (the hypotenuse), we can use trigonometry. Given the height of the ramp is 5 (the vertical side), and the angle of inclination is 4.8 degrees, we can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of inclination (4.8 degrees).
- Opposite is the height (5).
- Hypotenuse is the length of the ramp that we need to find.
Rearranging the formula to solve for the hypotenuse (length of the ramp), we have:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting in the values, we get:
\[ \text{hypotenuse} = \frac{5}{\sin(4.8^\circ)} \]
Now we calculate \(\sin(4.8^\circ)\):
\[ \sin(4.8^\circ) \approx 0.08354 \]
Therefore,
\[ \text{hypotenuse} = \frac{5}{0.08354} \approx 59.93 \]
Rounding to the nearest hundredth, the length of the ramp needed is approximately 59.93 units.
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