you are building a ramp that will be in the shape of a perfect right-angled triangle. The vertical height of th ramp will be 10 feet. the horizontal base of the ramp will be 15 feet. what will be the length of the downward sloping side of the ramp?

so you are finding the hypotenuse

solve for h

h^2 = 10^2 + 15^2

btw, what is a "perfect" right-angled triangle?

To find the length of the downward sloping side of the ramp, which is the hypotenuse of the right-angled triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the vertical height (opposite side) is 10 feet and the horizontal base (adjacent side) is 15 feet. Let's denote the hypotenuse as 'c'.

Using the Pythagorean theorem, we have:

c^2 = 10^2 + 15^2
c^2 = 100 + 225
c^2 = 325

To find 'c', we need to take the square root of both sides:

c = √(325)

Calculating the square root of 325 gives us:

c ≈ 18.027756377319946

Therefore, the length of the downward sloping side of the ramp is approximately 18.03 feet.