Question

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

Answer 1

30.33 is wrong

Answer 2

In the right triangle \( FCH \), you have \( FC = 33 \) cm and \( CH = 13 \) cm with a right angle at \( H \). To find the length of \( FH \), you can use the Pythagorean theorem, which states:

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

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides. In this case:

- \( a = FH \)
- \( b = CH = 13 \) cm
- \( c = FC = 33 \) cm

Thus, the equation becomes:

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

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

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

So the equation is:

\[
FH^2 + 169 = 1089
\]

Now, subtract \( 169 \) from both sides:

\[
FH^2 = 1089 - 169
\]
\[
FH^2 = 920
\]

Now, take the square root of both sides to find \( FH \):

\[
FH = \sqrt{920}
\]

Calculating the square root of \( 920 \):

\[
FH \approx 30.33 \, \text{cm}
\]

Therefore, the length of \( FH \) is approximately \( 30.33 \, \text{cm} \).

Answer 3

Let’s go through the calculations step by step to find the length of \( FH \) correctly.

You have a right triangle \( FCH \) with:

- \( FC = 33 \, \text{cm} \) (the hypotenuse)
- \( CH = 13 \, \text{cm} \) (one leg)

You want to find \( FH \) (the other leg). Using the Pythagorean theorem:

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

Substituting the known values:

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

Calculating the squares:

\[
FH^2 + 169 = 1089
\]

Now, subtract \( 169 \) from both sides:

\[
FH^2 = 1089 - 169
\]
\[
FH^2 = 920
\]

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

\[
FH = \sqrt{920}
\]

Calculating \( \sqrt{920} \):

\[
\sqrt{920} \approx 30.33 \, \text{cm}
\]

If this length seems incorrect based on specific criteria you need, please provide any additional details or context so I can assist you better!

Assuming my calculations were correct, \( FH \approx 30.33 \, \text{cm} \). If you have a specific expected value you can share, we can re-examine the calculations or the triangle setup.