For the square pyramid the lateral edge length is 25 in. and the slant height is 24 in. Find the height of the pyramid Round the answer to the nearest whole number. The height of the square pyramid is?
Let's use the Pythagorean theorem to find the height of the pyramid.
The lateral edge length is 25 in and the slant height is 24 in.
Let's label the height of the pyramid as "h".
The slant height represents the hypotenuse of a right triangle, with the height (h) and half of the lateral edge length (12.5 in) as the other two sides.
Using the Pythagorean theorem:
h^2 + (12.5)^2 = (24)^2
h^2 + 156.25 = 576
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides:
h ≈ √419.75
h ≈ 20.48
Rounding to the nearest whole number, the height of the pyramid is approximately 20 inches.
To find the height of the square pyramid, we can use the Pythagorean Theorem.
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 lateral edge length represents one of the sides and the slant height represents the hypotenuse of a right triangle. Let's denote the height of the pyramid as 'h'.
We can set up the equation as follows:
lateral edge length^2 + height^2 = slant height^2
(25 in)^2 + h^2 = (24 in)^2
625 + h^2 = 576
Now, subtract 576 from both sides of the equation:
h^2 = 576 - 625
h^2 = -49
Since we cannot take the square root of a negative number in this context, it means that there is no real height for the pyramid based on the given information.
To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height, the lateral edge length, and the height form a right triangle, where the slant height is the hypotenuse.
From the information given, we have:
Lateral edge length (a) = 25 in.
Slant height (c) = 24 in.
Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c^2 = a^2 + b^2
In this case, we want to find the height (b), so we rearrange the equation to solve for b:
b^2 = c^2 - a^2
Substituting the given values:
b^2 = 24^2 - 25^2
b^2 = 576 - 625
b^2 = -49
Since we cannot take the square root of a negative number, this means that there is no height that satisfies the given values. Therefore, there is no solution to this problem.