Question

th right triangles: practice
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?
door
ramp
2.3 feet
3.6 feet
2.3 feet
10.8 feet

Explanation:

Step1: Find ramp length (Pythagoras)

$$\text{Ramp length} = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13} \approx 3.606 \text{ ft}$$

Step2: Set up new distance equation

Let $x$ = new end distance. Use Pythagoras:
$$x = \sqrt{(\sqrt{13})^2 - 1.5^2}$$

Step3: Calculate new distance

$$x = \sqrt{13 - 2.25} = \sqrt{10.75} \approx 2.3 \text{ feet}$$

Answer:

2.3 feet