crystal wants to build a ramp that will rise 4ft over a horizontal distance of 20ft. how long will the ramp be? round to the nearest tenth.
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
4^2 + 20^2 = c^2
16 + 400 = c^2
416 = c^2
c = sqrt 416
c = 20.4
If you draw a picture, you'll end up with a right triangle, and the two shorter sides are a and b, and the hypotenuse (long side) is c.
Do you get it?
To find the length of the ramp, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the height of the ramp forms one side of the right triangle, and the horizontal distance forms the other side.
Let's label the length of the ramp as "c" (the hypotenuse), the height as "a," and the horizontal distance as "b." According to the Pythagorean theorem:
c^2 = a^2 + b^2
Given that the height (a) is 4ft and the horizontal distance (b) is 20ft, we can calculate the length of the ramp (c):
c^2 = 4^2 + 20^2
c^2 = 16 + 400
c^2 = 416
To find c, we need to take the square root of 416:
c = √416
c ≈ 20.396
Therefore, the length of the ramp is approximately 20.4ft when rounded to the nearest tenth.