# Any right triangle with hypotenuse z, the trigonometric function as: cosθ = x/z    sin θ= y/z   tan θ= y/xThe circle has a radius of 1

sciencesolve | Teacher | (Level 3) Educator Emeritus

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If you need to prove that hypotenuse of right triangle measures z, then you need to express the legs x and y in terms of z such that:

`x = z*cos theta`

`y = z*sin theta`

You need to remember that Pythagorean theorem tells that the sum of squares of legs of right triangle yields the square of hypotenuse, such that:

`x^2 + y^2 = z^2`

You need to substitute `z*cos theta ` for x and `z*sin theta`  for y such that:

`(z*cos theta)^2 + (z*sin theta)^2 = z^2`

You need to factor out `z^2 ` such that:

`z^2 (cos^2 theta + sin^2 theta) = z^2`

You need to remember the basic formula of trigonometry such that:

`cos^2 theta + sin^2 theta = 1`

Substsituting 1 for `cos^2 theta + sin^2 theta ` in Pythagorean theorem yields:

`z^2*1 = z^2`

Hence, using Pythagorean theorem and polar coordinates yields that hypotenuse of a right triangle, under given conditions,  measures z.