Question

If FC=33cm and CH=13cm the what is the length of FH in a triangle with a right angle at H

Answer 1

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 \( 30.33 \, \text{cm} \).