A ramp rises 5 feet and is 13 feet long. What horizontal distance h, in feet, does the ramp cover?
This is a job for Pythagoras.
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
b = 12
To find the horizontal distance h covered by the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the ramp, the vertical side is the rise of 5 feet, and the horizontal side is the distance h that we need to find.
Using the Pythagorean theorem, we have:
h^2 + 5^2 = 13^2
Simplifying,
h^2 + 25 = 169
Subtracting 25 from both sides,
h^2 = 144
Taking the square root of both sides,
h = √144
Since 144 is a perfect square (12^2), the square root of 144 is 12.
Therefore, the horizontal distance h covered by the ramp is 12 feet.