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
find the length of the height of the cone
To find the length of the height of the cone, we can use the Pythagorean theorem.
In this case, the height of the cone is the perpendicular side (a), the radius is the base side (b), and the slant height is the hypotenuse (c).
Using the formula a^2 + b^2 = c^2, we can substitute the given values:
a = 13 feet (height)
b = 5 feet (radius)
a^2 + b^2 = c^2
(13)^2 + (5)^2 = c^2
169 + 25 = c^2
194 = c^2
To find c, we take the square root of both sides:
√194 = √c^2
c ≈ 13.928
Therefore, the length of the height of the cone is approximately 13.928 feet.