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?
The picture of a right-angled triangle. The opposite and adjacent sidelines are extended. The length of the opposite side line up to the hypotenuse is 2 ft. and the adjacent side line up to the hypotenuse is 3 ft. The hypotenuse line is Ramp.
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the ramp x, and the height of the ramp y.
Using the Pythagorean theorem, we have:
x^2 = 2^2 + 3^2
x^2 = 4 + 9
x^2 = 13
x = √13
Now, we can set up a proportion to find the distance between the end of the ramp and the bus when the bus is lowered.
(1.5 / x) = (y / (x - 1.5))
Cross-multiplying this proportion, we have:
1.5(x - 1.5) = xy
1.5x - 2.25 = xy
Substituting the value of x (√13), we can simplify this equation:
1.5(√13) - 2.25 = y(√13)
√13(1.5 - 2.25) = y
√13(-0.75) = y
-0.75√13 = y
Thus, approximately, when the bus is lowered so that the door is 1.5 feet above the ground, the end of the ramp will be approximately -0.75√13 feet away from the bus.