Answer: [tex]b=\sqrt{c^{2}-a^{2}}[/tex]
Step-by-step explanation:
To solve the exercise you must solve for b from the formula for the hypotenuse, as you can see below:
- Square both sides of the equation as following:
[tex]c^{2}=(\sqrt{a^{2}+b^{2}})^{2}[/tex]
- Now you must subtract a² from each side of the equation, then you obtain:
[tex]c^2-a^{2}=a^{2}-a^{2}+b^{2}[/tex]
[tex]c^2-a^{2}=b^{2}[/tex]
- Apply square root to both sides:
[tex]\sqrt{b^{2}}=\sqrt{c^{2}-a^{2}}[/tex]
Then:
[tex]b=\sqrt{c^{2}-a^{2}}[/tex]
