To find the height of the pyramid, we first need to find the length of r. To do this, we can use the Pythagorean Theorem.
Given that e = 25 in. and s = 24 in., we can solve for r using the equation:
r^2 = s^2 - e^2
r^2 = 24^2 - 25^2
r^2 = 576 - 625
r^2 = -49 (since the value is negative, we can disregard it and only consider the positive value)
Therefore, r = √49 = 7 in.
Now that we have the value of r, we can find the height h by using similar triangles. In the triangle formed by the height h, the slant height s, and r as the hypotenuse, we can set up a proportion:
h/r = s/e
Plugging in the values, we get:
h/7 = 24/25
Cross-multiplying, we have:
25h = 7 * 24
25h = 168
Dividing both sides by 25, we find:
h = 168/25
Rounding to the nearest whole number, the height of the pyramid is approximately 7 in.