Question
What is the length of the missing leg? If necessary, round to the nearest tenth. a=58 c=48 b=?
Answers
GPT-4o mini
To find the length of the missing leg \( b \) in a right triangle, we can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is one leg of the triangle
- \( b \) is the other leg of the triangle
- \( c \) is the hypotenuse
Given:
- \( a = 58 \)
- \( c = 48 \)
- \( b = ? \)
Plugging in the values into the Pythagorean theorem:
\[
58^2 + b^2 = 48^2
\]
Calculating \( 58^2 \) and \( 48^2 \):
\[
58^2 = 3364
\]
\[
48^2 = 2304
\]
Now substituting these values back into the equation:
\[
3364 + b^2 = 2304
\]
To solve for \( b^2 \), we need to isolate \( b^2 \):
\[
b^2 = 2304 - 3364
\]
\[
b^2 = -1060
\]
Since \( b^2 \) cannot be negative, this indicates an invalid triangle with the provided lengths because the leg \( a \) (58) cannot be greater than the hypotenuse \( c \) (48).
Please check the values of \( a \) and \( c \) to confirm they correspond to a valid right triangle as per the Pythagorean theorem.
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is one leg of the triangle
- \( b \) is the other leg of the triangle
- \( c \) is the hypotenuse
Given:
- \( a = 58 \)
- \( c = 48 \)
- \( b = ? \)
Plugging in the values into the Pythagorean theorem:
\[
58^2 + b^2 = 48^2
\]
Calculating \( 58^2 \) and \( 48^2 \):
\[
58^2 = 3364
\]
\[
48^2 = 2304
\]
Now substituting these values back into the equation:
\[
3364 + b^2 = 2304
\]
To solve for \( b^2 \), we need to isolate \( b^2 \):
\[
b^2 = 2304 - 3364
\]
\[
b^2 = -1060
\]
Since \( b^2 \) cannot be negative, this indicates an invalid triangle with the provided lengths because the leg \( a \) (58) cannot be greater than the hypotenuse \( c \) (48).
Please check the values of \( a \) and \( c \) to confirm they correspond to a valid right triangle as per the Pythagorean theorem.