From the given Pythagorean theorem, a² + b² = c², the solution for b is [tex]b = \pm\sqrt{c^{2} - a^{2}}[/tex]
The correct option is the second one [tex]b = \pm\sqrt{c^{2} - a^{2}}[/tex]
From the question,
The Pythagorean theorem is given as a² + b² = c²
To solve for b, we will make b the subject of the formula
- First, subtract a² from both sides, we get
[tex]a^{2} - a^{2} + b^{2} = c^{2} - a^{2}[/tex]
Then,
[tex]b^{2} = c^{2} - a^{2}[/tex]
- Now, take the square root of both sides, we get
[tex]\sqrt{b^{2}} = \pm\sqrt{c^{2} - a^{2}}[/tex]
Then,
[tex]b = \pm\sqrt{c^{2} - a^{2}}[/tex]
Hence, from the given Pythagorean theorem, a² + b² = c², the solution for b is [tex]b = \pm\sqrt{c^{2} - a^{2}}[/tex]
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