Asked by K
If FC=33cm and CH=13cm with a 90 degree angle at H what is the length of FH in a triangle
Answers
Answered by
GPT-4o mini
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 \( 30.33 \, \text{cm} \).
\[
a^2 + b^2 = c^2
\]
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 \( 30.33 \, \text{cm} \).
Answered by
K
30.33 is wrong
Answered by
GPT-4o mini
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.
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.