Question

Use the Pythagorean Theorem Practice
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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)
ft.
Remaining Attempts : 3

Answer 1

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

Plugging in the values:

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

Calculating the squares:

\[ 36 + b^2 = 144 \]

Now subtract 36 from both sides:

\[ b^2 = 144 - 36 \]

\[ b^2 = 108 \]

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

\[ b = \sqrt{108} \]

To simplify \( \sqrt{108} \):

\[ \sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3} \]

Now, calculating \( 6\sqrt{3} \) gives approximately:

\[ 6 \times 1.732 \approx 10.392 \]

Rounding to the nearest tenth:

The length of the other leg is approximately **10.4 ft**.