Question

according to the guidelines set by the ada, wheelchair ramps should be built at an angle of no more than (4.8^{circ}). if a contractor is designing a wheelchair ramp for a doorway that is 5 feet above ground level, which equation could be used to determine the length of the shortest possible ramp to reach the doorway?
3 of 12 question
(\frac{sin4.8^{circ}}{5}=\frac{sin85.2^{circ}}{x})
(\frac{sin85.2^{circ}}{5}=\frac{sin4.8^{circ}}{x})
(\frac{sin4.8^{circ}}{5}=\frac{sin90^{circ}}{x})
(\frac{sin85.2^{circ}}{5}=\frac{sin90^{circ}}{x})

Explanation:

Step1: Analyze the triangle

The doorway height (5 feet) is the side opposite the angle of \(4.8^{\circ}\). The ramp length \(x\) is the hypotenuse. The other non - right angle in the right - triangle is \(90^{\circ}-4.8^{\circ}=85.2^{\circ}\).

Step2: Apply the sine rule

In a triangle, the sine rule states that \(\frac{\sin A}{a}=\frac{\sin B}{b}\). In a right - triangle (angle \(C = 90^{\circ}\)), if \(A = 4.8^{\circ}\), \(a = 5\) (opposite side) and \(C=90^{\circ}\), \(c=x\) (hypotenuse). But we can also use the fact that \(\frac{\sin(85.2^{\circ})}{5}=\frac{\sin(90^{\circ})}{x}\) (since the side of length 5 is opposite the \(85.2^{\circ}\) angle and \(x\) is opposite the \(90^{\circ}\) angle in the right - triangle).

Answer:

\(\frac{\sin85.2^{\circ}}{5}=\frac{\sin90^{\circ}}{x}\) (the fourth option)