To find the length of FH, we can use the information provided. We have:
- FC = 33 cm (the radius from the center C to point F)
- CH = 13 cm (the radius from the center C to point H)
Since both FC and CH are radii of the same circle, we can visualize that F and H are points on the circumference at different distances from the center C.
To find the length of FH, we can use the right triangle formed by points F, H, and C. According to the Pythagorean theorem, we can set the equation:
\[ FH^2 = FC^2 - CH^2 \]
Substituting the known values into the equation:
\[ FH^2 = 33^2 - 13^2 \]
Calculating these squares:
\[ 33^2 = 1089 \] \[ 13^2 = 169 \]
So now we substitute these values back:
\[ FH^2 = 1089 - 169 = 920 \]
Now, take the square root to find FH:
\[ FH = \sqrt{920} \approx 30.33 \]
Rounding to the nearest centimeter:
\[ FH \approx 30 \text{ cm} \]
Therefore, the length of FH to the nearest centimeter is 30 cm.