Question

a city bus has a wheelchair ramp. when the bus is raised so that the door is 2 feet above the ground, the end of the ramp is 3 feet away from the bus. if the bus is lowered so the door is 1.5 feet above the ground, approximately how far away will the end of the ramp be from the bus? 10.8 feet 3.3 feet 2.3 feet 3.6 feet

Explanation:

Step1: Set up proportion

Since the two right - angled triangles formed by the ramp are similar, the ratios of their corresponding sides are equal. Let the initial height be $h_1 = 2$ ft, the initial base be $b_1 = 3$ ft, the new height be $h_2=1.5$ ft, and the new base be $b_2$. The proportion is $\frac{h_1}{b_1}=\frac{h_2}{b_2}$.

Step2: Substitute values

Substitute $h_1 = 2$, $b_1 = 3$, and $h_2 = 1.5$ into the proportion $\frac{2}{3}=\frac{1.5}{b_2}$.

Step3: Solve for $b_2$

Cross - multiply: $2b_2=1.5\times3$. Then $2b_2 = 4.5$. Divide both sides by 2: $b_2=\frac{4.5}{2}=2.25\approx2.3$ ft.

Answer:

2.3 feet