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.