A construction worker needs to build a ramp for wheelchair access. If the height of the entrance is 3 feet and the ramp must create an angle of \( 30^{\circ} \) with the ground, what is the length of the ramp?

To determine the length of the ramp needed for wheelchair access, we can use trigonometry, specifically the sine function, which relates the angle of elevation to the ratio of the opposite side (height) to the hypotenuse (ramp length) in a right-angled triangle. **Given:** - Height of the entrance (\( \text{opposite} \)) = 3 feet - Angle with the ground (\( \theta \)) = \( 30^{\circ} \) **Using the sine function:** \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] Plugging in the known values: \[ \sin(30^{\circ}) = \frac{3 \text{ feet}}{\text{hypotenuse}} \] We know that \( \sin(30^{\circ}) = 0.5 \). Therefore: \[ 0.5 = \frac{3}{\text{hypotenuse}} \] Solving for the hypotenuse: \[ \text{hypotenuse} = \frac{3}{0.5} = 6 \text{ feet} \] **Conclusion:** The ramp needs to be **6 feet** long to achieve a \( 30^{\circ} \) angle with the ground. **Answer:** The ramp must be 6 feet long.