Observe the cone figure below. The slant height, l, is the diagonal length of the cone. The cone stands 13 feet tall and has a radius of 5, what is the length of the height of the cone? a2 +b2 = c2 length of the height equals?
To find the length of the height of the cone, we can use 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 lengths of the other two sides (a and b).
In this case, we can consider the slant height (l) as the hypotenuse, the height (h) as one side, and the radius (r) as the other side.
Given that the slant height (l) is the diagonal length of the cone, and by considering the height (h) and the radius (r) as the other two sides of a right triangle, we have:
l² = h² + r²
Plugging in the given values, h = 13 feet and r = 5 feet, we can solve for the length of the height (h):
l² = h² + r²
l² = 13² + 5²
l² = 169 + 25
l² = 194
Taking the square root of both sides, we get:
l = √194
Therefore, the length of the height (h) of the cone is approximately equal to √194 feet.