Question

What is the length of the missing leg? If necessary, round to the nearest tenth. a=58 c=48 b=?
can u find the length of b?

Answer 1

To find the length of the missing leg \( b \) in a right triangle where \( a \) and \( c \) are known, we can use the Pythagorean theorem:

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

where
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the two legs.

Given:
- \( a = 58 \)
- \( c = 48 \)

First, substitute the values into the Pythagorean theorem:

\[
48^2 = 58^2 + b^2
\]

Calculating \( 48^2 \) and \( 58^2 \):

\[
48^2 = 2304
\]
\[
58^2 = 3364
\]

Now, substitute these values into the equation:

\[
2304 = 3364 + b^2
\]

Now, solve for \( b^2 \):

\[
b^2 = 2304 - 3364
\]
\[
b^2 = -1060
\]

Since \( b^2 \) is negative, it indicates that a triangle cannot exist with these side lengths (specifically \( a \) cannot be larger than \( c \) for a right triangle).

Since \( a \) must be shorter than \( c \) in a right triangle, please double-check the assigned values of \( a \) and \( c \). If \( c \) is indeed the hypotenuse, then we need \( a \) to be shorter than \( c \).

If there's an error in the values provided, please correct it, and I can help you find the correct length of \( b \).