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 \( b \).
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