Question

If a right triangle has a leg that is 6ft long and the hypotenuse is 12ft long how long is the other leg? Round to the nearest tenth

Answer 1

To find the length of the other 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, and \(a\) and \(b\) are the lengths of the legs. In this case, one leg \(a = 6\) ft, and the hypotenuse \(c = 12\) ft. We need to find the length of the other leg \(b\).

Substituting the known values into the Pythagorean theorem:

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

Calculating \(6^2\) and \(12^2\):

\[
36 + b^2 = 144
\]

Now, subtract \(36\) from both sides:

\[
b^2 = 144 - 36
\]

\[
b^2 = 108
\]

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

\[
b = \sqrt{108}
\]

Calculating \(\sqrt{108}\):

\[
b = \sqrt{36 \times 3} = 6\sqrt{3}
\]

Now, approximate \(6\sqrt{3}\):

\[
\sqrt{3} \approx 1.732
\]

So,

\[
b \approx 6 \times 1.732 \approx 10.392
\]

Rounding to the nearest tenth:

\[
b \approx 10.4 \text{ ft}
\]

Therefore, the length of the other leg is approximately **10.4 ft**.