We can use the Pythagorean theorem to solve for the height of the pyramid.
The Pythagorean theorem 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 slant height is the hypotenuse, and the height and half of the base are the other two sides.
We can set up the equation as follows:
height^2 + (base/2)^2 = slant height^2
height^2 + (22.6/2)^2 = 88.9^2
height^2 + 256.03 = 7921
height^2 = 7664.97
height = 87.6 in (rounded to the nearest tenth)
Therefore, the height of the pyramid is approximately 87.6 inches.