Question

21.) a = 3, b = ???, c = \sqrt{58}

Explanation:

Assuming this is a right - triangle problem with \(c\) as the hypotenuse, we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).

Step 1: Substitute the known values

We know that \(a = 3\) and \(c=\sqrt{58}\). Substituting these values into the Pythagorean theorem, we get \(3^{2}+b^{2}=(\sqrt{58})^{2}\).

Step 2: Simplify the equation

Simplify both sides of the equation. \(3^{2}=9\) and \((\sqrt{58})^{2}=58\). So the equation becomes \(9 + b^{2}=58\).

Step 3: Solve for \(b^{2}\)

Subtract 9 from both sides of the equation: \(b^{2}=58 - 9=49\).

Step 4: Solve for \(b\)

Take the square root of both sides. Since \(b\) represents a length (in the context of a triangle side), we take the positive square root. So \(b=\sqrt{49} = 7\).

Answer:

\(b = 7\)