What is the length of the missing leg? If necessary, round to the nearest tenth.




























a
=
inches

b = 20, c = 12

1 answer

To find the length of the missing leg \( a \) in a right triangle with legs \( b \) and \( c \), you can use the Pythagorean theorem, which states:

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

Here, \( b \) is one leg, \( c \) is the hypotenuse, and \( a \) is the other leg you want to find. Given your values:

  • \( b = 20 \) inches
  • \( c = 12 \) inches

Since \( c \) should be the hypotenuse, it should be the longest side. However, in this case, it seems like there is a mismatch because 20 > 12; thus it doesn't comply with the Pythagorean theorem.

Assuming you meant:

  • \( a = 20 \) inches (the hypotenuse)
  • \( b = 12 \) inches (one leg)

We can rearrange the Pythagorean theorem:

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

Let's recalculate it under the assumption that \( c \) is the missing leg:

\[ a = 20, \quad b = 12 \]

Then:

\[ 20^2 = 12^2 + c^2 \]

Calculating the squares:

\[ 400 = 144 + c^2 \]

Now, isolate \( c^2 \):

\[ c^2 = 400 - 144 \] \[ c^2 = 256 \]

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

\[ c = \sqrt{256} = 16 \text{ inches} \]

Thus, the length of the missing leg \( c \) is \( 16 \) inches.