Pythagorean theorem and trig ratios

Question

How does the Pythagorean Theorem relate to trigonometric ratios?

Answer 1

The unit circle is quite useful and it helps to understand the trigonometric identities. This is because the hypotenuse is always 1.

With the hypotenuse of a right triangle always 1, the two length of the two legs (the x and the y on a graph) are fixed for any given angle of the hypotenuse. Thus, the trigonometric ratios may be quickly evaluated.

The Pythagorean Theorem allows us to determine the lengths of the two legs of the right triangle.

Answer 2

Are you are referring to the 45-45-90 triangle that uses the ratios 1-1- √2?

If you use the Pythagorean theorem for this the 1 and 1 would be the legs.

1²+1²=c²

1+1=c²

2=c²

Take the square root of both sides,

√2 = c, which matches the Pythagorean Theorem.

The same will work for 30-60-90 (1-√3 -2)