Question
length of other leg of right triangle with one leg 8 inches and hypotenuse 12 inches using Pythagorean Theorem
Answers
GPT-4o mini
To find the length of the other leg of a right triangle using the Pythagorean Theorem, you can use the formula:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
In your case:
- One leg (\( a \)) = 8 inches
- Hypotenuse (\( c \)) = 12 inches
We need to find the length of the other leg (\( b \)). Rearranging the formula gives:
\[ b^2 = c^2 - a^2 \]
Now, substituting the known values:
\[ b^2 = 12^2 - 8^2 \]
\[ b^2 = 144 - 64 \]
\[ b^2 = 80 \]
Now, taking the square root of both sides:
\[ b = \sqrt{80} \]
\[ b = \sqrt{16 \times 5} \]
\[ b = 4\sqrt{5} \]
So, the length of the other leg is \( 4\sqrt{5} \) inches, which is approximately 8.94 inches.
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
In your case:
- One leg (\( a \)) = 8 inches
- Hypotenuse (\( c \)) = 12 inches
We need to find the length of the other leg (\( b \)). Rearranging the formula gives:
\[ b^2 = c^2 - a^2 \]
Now, substituting the known values:
\[ b^2 = 12^2 - 8^2 \]
\[ b^2 = 144 - 64 \]
\[ b^2 = 80 \]
Now, taking the square root of both sides:
\[ b = \sqrt{80} \]
\[ b = \sqrt{16 \times 5} \]
\[ b = 4\sqrt{5} \]
So, the length of the other leg is \( 4\sqrt{5} \) inches, which is approximately 8.94 inches.