A stainless steel patio heater is a square pyramid. The length of one side of the base is 20.8 inches.The slant height of the pyramid is 89.1inch.What is the height of the pyramid?
To find the height of the pyramid, we can use the Pythagorean theorem, as the slant height, base length, and height of the pyramid form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the slant height (hypotenuse) is 89.1 inches, and one side of the base is 20.8 inches.
Let's denote the height of the pyramid as "h." As the base of the pyramid is a square, all sides are equal, so the other side of the base is also 20.8 inches.
Using the Pythagorean theorem, we can set up the equation:
(20.8)^2 + h^2 = (89.1)^2
Simplifying the equation:
(433.64) + h^2 = 7932.81
Subtracting 433.64 from both sides:
h^2 = 7932.81 - 433.64
h^2 = 7499.17
Taking the square root of both sides to solve for h:
h ≈ √7499.17
h ≈ 86.6 inches
Therefore, the approximate height of the pyramid is 86.6 inches.
the slant height is the hypotenuse of a right triangle
... consisting of the height, slant height and half of the diagonal of the base
89.1^2 = h^2 + (20.8 √2 / 2)^2