Question

If a right triangle has a leg that
is 6 ft. long and the
hypotenuse is 12 ft. long, how
long is the other leg? Round
to the nearest tenth. (1 point)

Answer 1

To find the length of the other leg in a right triangle given one leg and the hypotenuse, 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 legs of the triangle.

In this case, you have:
- One leg \(a = 6\) ft
- Hypotenuse \(c = 12\) ft
- Let the other leg be \(b\)

Substituting into the equation:

\[ 6^2 + b^2 = 12^2 \]

This simplifies to:

\[ 36 + b^2 = 144 \]

Now, subtract 36 from both sides to isolate \(b^2\):

\[ b^2 = 144 - 36 \]
\[ b^2 = 108 \]

Now, take the square root of both sides to find \(b\):

\[ b = \sqrt{108} \]
\[ b \approx 10.3923 \]

Rounding to the nearest tenth, the length of the other leg is approximately:

**10.4 ft**.