A loading ramp is 2.8m long. One end rests on a loading dock 0.7 meters above the ground, and the other end leads into the back of a a tractor trailer 1.2m above the ground. Find the horizontal distance between the back of the truck and the loading dock, to the nearest tenth of a meter.
a² + b² = c²
The Attempt at a Solution
In order to solve this problem I figured out that you need to make an imaginary hypotenuse from the ground below the truck to the top of the loading dock. With that hypotenuse you need to figure out the horizontal distance between the back of the truck and the loading dock.
Let x represent the diagonal from the ground at the truck to the loading dock.
2.8^2 - .7^2 = x^2
√6.4 = √x^2
2.53m = x
That is for the imaginary hypotenuse. Now for the leg it asked for:
Let h represent the horizontal distance between the back of the truck to the start of the dock.
2.53^2 - .7^2 = h^2
6.4 - .49 = h^2
√5.91 = √h^2
2.43m = h
Then the therefor statement. The problem is, the textbook tells me the answer is 2.8. Where did I go wrong?
To get a mental image, just imagine a rectangle with a diagonal from the lower left corner to the upper right corner.