Question

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































a
=
inches

b = 20, c = 12

Answer 1

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.