Answer:
b = [tex]\sqrt{333}[/tex]
Step-by-step explanation:
1. We can use the Pythagorean Theorem to find the missing side, b.
- [tex]14^2 + b^2 = 23^2[/tex]
2. (Solving)
Step 1: Simplify both sides of the equation.
- [tex](14*14)+b^2 =(23*23)[/tex]
- [tex]196 + b^2 = 529[/tex]
Step 2: Subtract 196 from both sides.
- [tex]196 + b^2 - 196 = 529 - 196[/tex]
- [tex]b^2 = 333[/tex]
Step 3: Take square root of both sides.
- [tex]\sqrt{b^2} = \sqrt{333}[/tex]
- [tex]b = \sqrt{333}[/tex]
Step 4: Check if solution is correct.
- [tex]14^2 + \sqrt{333^2} = 23^2[/tex]
- [tex](14*14)+(\sqrt{333} *\sqrt{333})=23*23[/tex]
- [tex]196 + 333 = 529[/tex]
- [tex]529 = 529[/tex]
Therefore, b = [tex]\sqrt{333}[/tex].
