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, we can use trigonometry. The relationship involves the height of the entrance, the angle of the ramp, and the length of the ramp itself. We use the sine function defined as: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] In this case, the height of the entrance (3 feet) is the "opposite" side, and the length of the ramp is the "hypotenuse". Thus, we have: \[ \sin(30^{\circ}) = \frac{3 \text{ feet}}{L} \] Since \(\sin(30^{\circ}) = \frac{1}{2}\), we can substitute and rearrange the equation: \[ \frac{1}{2} = \frac{3}{L} \] Cross-multiplying gives us: \[ L = 3 \times 2 = 6 \text{ feet} \] Thus, the length of the ramp is 6 feet.