In a right triangle \( FCH \) with a right angle at \( H \), we can use the Pythagorean theorem to find the length of \( FH \).
According to the Pythagorean theorem:
\[ FC^2 = FH^2 + CH^2 \]
Where:
- \( FC = 33 , \text{cm} \)
- \( CH = 13 , \text{cm} \)
Substituting the values into the equation:
\[ 33^2 = FH^2 + 13^2 \]
Calculating the squares:
\[ 1089 = FH^2 + 169 \]
Now, subtract \( 169 \) from both sides:
\[ 1089 - 169 = FH^2 \]
\[ 920 = FH^2 \]
Now, take the square root of both sides to find \( FH \):
\[ FH = \sqrt{920} \]
Calculating \( \sqrt{920} \):
\[ FH \approx 30.33 , \text{cm} \]
Therefore, the length of \( FH \) is approximately \( 30.33 , \text{cm} \).