Question

The formula for the hypotenuse of a right triangle with legs of length a and b is shown.

What is b in terms of a and c?

Answer 1

see explanation

Explanation:

Given

c =
`√(a^2+b^2)`

Square both sides

c² = a² + b² ( subtract a² from both sides )

c² - a² = b² ( take the square root of both sides )

`√(c^2-a^2)` = b

⇒ b =
`√(c^2-a^2)`

Answer 2

Answer:
`b=\sqrt{c^(2)-a^(2)}`

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:

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

- Now you must subtract a² from each side of the equation, then you obtain:

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

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

- Apply square root to both sides:

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

Then:

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