Question

A stainless steel patio heater is a square pyramid. The length of one side of the base is 19.4 in.19.4 in. The slant height of the pyramid is 91.5 in.91.5 in. What is the height of the​ pyramid?

Answer 1

Answer:

89.4 inches

Step-by-step explanation:

The slant height of the square pyramid, the height of the square pyramid and half the base side of the square pyramid altogether form a right triangle.

In this right triangle, the slant height is the hypotenuse.

By the Pythagorean theorem,

$91.5^2=19.4^2+h^2\\ \\h^2=91.5^2-19.4^2\\ \\h^2=8,372.25-376.36\\ \\h^2=7,995.89\\ \\h=\sqrt{7,995.89}\ in\\ \\h\approx 89.4\ in$