To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, we know:
- One leg \( a = 12 \)
- The hypotenuse \( c = 16 \)
- We need to find the length of the other leg \( b \).
Plugging the known values into the equation gives us:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Next, we isolate \( b^2 \) by subtracting 144 from both sides:
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Now, we take the square root of both sides to solve for \( b \):
\[ b = \sqrt{112} \]
Calculating the square root:
\[ b \approx 10.583 \]
Rounding to the nearest tenth gives:
\[ b \approx 10.6 \]
Thus, the length of the other leg is approximately 10.6.
1 answer