Question

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

Answer 1

Answer: $b=\sqrt{c^{2}-a^{2}}$

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:

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

- 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:

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

Answer 2

Answer:

see explanation

Step-by-step explanation:

Given

c = $\sqrt{a^2+b^2}$

Square both sides

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

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

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

⇒ b = $\sqrt{c^2-a^2}$