Use the Pythagorean Theorem Practice

Question

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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

Answer 1

To find the length of the other leg of the right triangle, you can use the Pythagorean Theorem, which states:

\[ a^2 + b^2 = c^2 \]

where \( a \) and \( b \) are the legs of the triangle and \( c \) is the hypotenuse.

In this problem, we have:

• One leg \( a = 6 \) ft
• Hypotenuse \( c = 12 \) ft
• We need to find the other leg \( b \).

Substituting the known values into the equation:

\[ 6^2 + b^2 = 12^2 \] \[ 36 + b^2 = 144 \]

Now, subtract 36 from both sides:

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

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

\[ b = \sqrt{108} \] \[ b = \sqrt{36 \times 3} \] \[ b = 6\sqrt{3} \]

Now calculating \( 6\sqrt{3} \):

Using \( \sqrt{3} \approx 1.732 \):

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

Rounding to the nearest tenth:

The length of the other leg is approximately 10.4 ft.