A stainless steel patio heater is a square pyramid. The length of one side of the base is 21.6 inches. The slant height of the pyramid is 83.3 inches. What is the height of the pyramid? Round to one decimal place as needed.
I have tried and can't figure it out.
To find the height of the pyramid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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 of the pyramid is the hypotenuse, and the height of the pyramid is one of the other sides. The length of one side of the base is the other side of the right triangle.
Let's call the height of the pyramid "h" and the length of one side of the base "s".
According to the Pythagorean theorem, we have:
s^2 + h^2 = (slant height)^2
Plugging in the given values, we get:
21.6^2 + h^2 = 83.3^2
Now we can solve for h:
h^2 = 83.3^2 - 21.6^2
h^2 = 6932.89 - 466.56
h^2 = 6466.33
Taking the square root of both sides, we find:
h ≈ √(6466.33)
h ≈ 80.4 inches
Therefore, the height of the pyramid is approximately 80.4 inches.
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Your friend says that the volume of a sphere is 407.51. Use 3.14 for p. What mistake might your friend have made? Type a whole number or decimal. Round to nearest hundredth as needed. The radius is 4.6
the height forms a right triangle with the slant height as the hypotenuse and half of the base diagonal as the other leg
(height)^2 = (slant height)^2 - (half of base diagonal)^2
h^2 = 83.3^2 - (10.8 √2)^2