Question

A^2 b^2=c^2 express b in terms of a and c

Answer 1

Answer:

$b=\dfrac{c}{a}\ or\ b=\sqrt{c^2-a^2}$

Step-by-step explanation:

$If\ is\ a^2b^2=c^2:\\\\a^2b^2=c^2\qquad\text{divide both sides by}\ a^2\neq0\\\\b^2=\dfrac{c^2}{a^2}\to b=\sqrt{\dfrac{c^2}{a^2}}\\\\b=\dfrac{\sqrt{c^2}}{\sqrt{a^2}}\\\\\boxed{b=\dfrac{c}{a}}$

$If\ is\ a^2+b^2=c^2:\\\\a^2+b^2=c^2\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\b^2=c^2-a^2\to\boxed{b=\sqrt{c^2-a^2}}$