If FC=33cm and CH=13cm the what is the length of FH in a triangle with a 90 degree angle at H

Answer 1

To find the length of \( FH \) in a right triangle \( FCH \) where the right angle is at \( H \), you can use the Pythagorean theorem. The theorem states:

\[ a^2 + b^2 = c^2 \]

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.

In this triangle:

• Let \( FC \) be one leg (33 cm).
• Let \( CH \) be the other leg (13 cm).
• Let \( FH \) be the length we want to find, which will be the hypotenuse.

Now, substitute the known values into the Pythagorean theorem:

\[ FH^2 = FC^2 + CH^2 \]

\[ FH^2 = (33)^2 + (13)^2 \]

Calculating \( 33^2 \) and \( 13^2 \):

\[ 33^2 = 1089 \] \[ 13^2 = 169 \]

Now add these values:

\[ FH^2 = 1089 + 169 = 1258 \]

Now take the square root to find \( FH \):

\[ FH = \sqrt{1258} \]

Calculating \( \sqrt{1258} \):

\[ FH \approx 35.5 \text{ cm} \]

Thus, the length of \( FH \) is approximately \( 35.5 \) cm.

Answer 2

35.5 is wrong

Answer 3

Apologies for the mistake. Let's go through the calculation step by step again.

We have the lengths:

• \( FC = 33 \text{ cm} \)
• \( CH = 13 \text{ cm} \)

In triangle \( FCH \), where angle \( H \) is a right angle, we can use the Pythagorean theorem:

\[ FH^2 = FC^2 + CH^2 \]

Calculating \( FC^2 \) and \( CH^2 \):

\[ FC^2 = 33^2 = 1089 \]

\[ CH^2 = 13^2 = 169 \]

Now, we add these values together:

\[ FH^2 = 1089 + 169 = 1258 \]

Now, we find \( FH \) by taking the square root:

\[ FH = \sqrt{1258} \]

Upon calculating:

\[ FH \approx 35.5 \text{ cm} \]

This calculation is indeed correct, and \( FH \) is approximately \( 35.5 \) cm.

If there's still an issue or if you meant something else, please let me know.