#### Answer

In a Right Triangle, where x is height, y is base and z is hypotenuse, Pythagoras theorem is:
$x^{2}+y^{2}=z^{2}$
Refer to the step-by-step part for the explanation.

#### Work Step by Step

Let the angle between z(hypotenuse) and y(base) in a right angled triangle be $\theta$
Step 1: By identity, $\sin^{2}\theta+\cos^{2}\theta=1$
Step 2: By definition,
$\sin\theta= \frac{\text{OppositeSide}}{\text{Hypotenuse}}$ and
$\cos\theta= \frac{\text{AdjacentSide}}{\text{Hypotenuse}}$
Therefore,
$\sin^{2}\theta+\cos^{2}\theta= \frac{\text{OppositeSide}^{2}}{\text{Hypotenuse}^{2}}+\frac{\text{AdjacentSide}^{2}}{\text{Hypotenuse}^{2}}$ =1
Step 3: The opposite side is $x$ and adjacent side is $y$, therefore,
$\sin^{2}\theta+\cos^{2}\theta= \frac{x^{2}}{z^{2}}+\frac{y^{2}}{z^{2}}=1 $
Step 4: Add the numerators and copy the common denominator:
$\frac{x^{2}+y^{2}}{z^{2}}=1$
Step 5: Cross multiplication,
$x^{2}+y^{2}=z^{2}$ (Pythagorean Theorem)