Question

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






























a
=
inches

b = 13, c = 12

Answer 1

To find the length of the missing leg \( a \) of a right triangle, given that \( b = 13 \) inches and \( c = 12 \) inches, we can use the Pythagorean theorem, which states:

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

In this case, \( b \) is one leg of the triangle and \( c \) is the hypotenuse. Let's plug in the given values:

\[
a^2 + 13^2 = 12^2
\]

Calculating the squares:

\[
a^2 + 169 = 144
\]

Now, we solve for \( a^2 \):

\[
a^2 = 144 - 169
\]
\[
a^2 = -25
\]

At this point, we see that \( a^2 \) cannot be negative, which indicates that the lengths given do not correspond to a valid right triangle, given the definition of a right triangle where the hypotenuse must be the longest side.

Thus, we conclude there is a mistake in the provided values as \( c \) (hypotenuse) should be greater than either leg \( a \) or \( b \), but here, \( 12 < 13 \).

If you're looking for \( a \) in the context where \( c \) is the hypotenuse, you might need to confirm the values of \( b \) and \( c \). If your setup is reversed and you meant \( c = 13 \) as the hypotenuse, then the equation would look like:

\[
a^2 + 12^2 = 13^2
\]

Calculating it in that scenario:

\[
a^2 + 144 = 169
\]
\[
a^2 = 169 - 144
\]
\[
a^2 = 25
\]
\[
a = \sqrt{25} = 5
\]

So, if \( c = 13 \) and \( b = 12 \), then the length of the missing leg \( a \) is \( 5 \) inches.

Please clarify the values if this doesn't resolve your question!