Apply the Pythagorean theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth one side is 25 ft and the bottom is 40 ft

Answer 1

To apply the Pythagorean theorem, we need to identify the two legs and the hypotenuse of the right triangle formed by the height of the square pyramid.

In this case, one leg of the right triangle is the height of the pyramid, h, and another leg is half the length of the base, which is 40/2 = 20 ft.

Let's label the hypotenuse as c.

According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

So we have: h^2 + 20^2 = c^2

Now, substitute the given values: h^2 + 400 = c^2

To isolate the height, h, we need to solve for it:

h^2 = c^2 - 400

Taking the square root of both sides, we get:

h = sqrt(c^2 - 400)

Now, we are given that one side of the square pyramid is 25 ft, which will be one of the slant heights of the triangular faces. To find c, we can use the Pythagorean theorem again:

c^2 = 25^2 + 20^2
c^2 = 625 + 400
c^2 = 1025

Taking the square root of both sides, we get:

c = sqrt(1025)
c ≈ 32.02

Now we can substitute this value of c into the equation for h:

h = sqrt(c^2 - 400)
h = sqrt((32.02)^2 - 400)
h ≈ sqrt(1024.16 - 400)
h ≈ sqrt(624.16)
h ≈ 24.97

Rounding to the nearest tenth, the height of the square pyramid, h, is approximately 25.0 ft.