Question

One side is 13 and the other Is 10 Find the length of the height of the cone

Answer 1

To find the height of a cone when you know the lengths of the two sides, it seems like you might be referencing a right triangle formed by the radius, height, and slant height of the cone.

Assuming that:
- One side (10) is the radius (r) of the base of the cone,
- The other side (13) is the slant height (l) of the cone,

You can use the Pythagorean theorem to find the height (h) of the cone:

\[
l^2 = r^2 + h^2
\]

Substituting the values you provided:

\[
13^2 = 10^2 + h^2
\]

Calculating the squares:

\[
169 = 100 + h^2
\]

Now, subtract 100 from both sides:

\[
169 - 100 = h^2
\]

\[
69 = h^2
\]

Now, take the square root of both sides to find h:

\[
h = \sqrt{69} \approx 8.31
\]

So, the height of the cone is approximately 8.31 units.