apply the pythagorean theorem to determine the height of the square pyramid, h. round the answer to the nearest tenth.
the slant height is 25 ft and the base is 40 ft
To determine the height of the square pyramid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.
In this case, the slant height of the pyramid is the hypotenuse, and the base of the pyramid is one of the other sides. Let's call the height of the pyramid "h".
Using the Pythagorean theorem, we can set up the following equation:
h^2 + (base/2)^2 = slant height^2
Substituting the given values:
h^2 + (40/2)^2 = 25^2
Simplifying the equation:
h^2 + 20^2 = 25^2
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides:
h = √225
h = 15
Therefore, the height of the square pyramid is 15 ft.