The formula c=\sqrt{a^(2)+b^(2) } represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for b. Show your work.

Question

The formula c=
`\sqrt{a^(2)+b^(2) }` represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for b. Show your work.

Answer 1

The required equation is
`b=√(c^2-a^2)`

Explanation:

Consider the provided equation.

`c= \sqrt{a^(2)+b^(2)}`

Solve the equation for b.

Square both the sides.

`c^2= a^(2)+b^(2)`

Subtract a² from both the sides.

`c^2-a^2= b^(2)`

Square root both the sides.

`b=√(c^2-a^2)`

Hence the required equation is
`b=√(c^2-a^2)`