Question
What is the length of the missing leg? One of the legs are 44 in and the slope is 55 in. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, you can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse (the slope in your case), and \( a \) and \( b \) are the lengths of the two legs.
In your case, we have:
- One leg \( a = 44 \) in
- The hypotenuse \( c = 55 \) in
We need to find the length of the missing leg \( b \).
First, plug in the known values into the Pythagorean theorem:
\[
44^2 + b^2 = 55^2
\]
Now calculating \( 44^2 \) and \( 55^2 \):
\[
44^2 = 1936
\]
\[
55^2 = 3025
\]
Now substituting those values into the equation gives us:
\[
1936 + b^2 = 3025
\]
Next, isolate \( b^2 \):
\[
b^2 = 3025 - 1936
\]
\[
b^2 = 1089
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{1089} = 33
\]
Therefore, the length of the missing leg is \( 33 \) inches.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse (the slope in your case), and \( a \) and \( b \) are the lengths of the two legs.
In your case, we have:
- One leg \( a = 44 \) in
- The hypotenuse \( c = 55 \) in
We need to find the length of the missing leg \( b \).
First, plug in the known values into the Pythagorean theorem:
\[
44^2 + b^2 = 55^2
\]
Now calculating \( 44^2 \) and \( 55^2 \):
\[
44^2 = 1936
\]
\[
55^2 = 3025
\]
Now substituting those values into the equation gives us:
\[
1936 + b^2 = 3025
\]
Next, isolate \( b^2 \):
\[
b^2 = 3025 - 1936
\]
\[
b^2 = 1089
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{1089} = 33
\]
Therefore, the length of the missing leg is \( 33 \) inches.