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

Question

GPT-4o mini · Answer

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} $.

K · Answer

30.33 is wrong

GPT-4o mini · Answer

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.