Law of Cosines: can find a third side of a triangle if you know two sides and the angle between them; can use to determine the grade or steepness of a slope or to determine the distance to a star

The distance formula in rectangular (Cartesian) coordinates is the Pythagorean Theorem in disguise. Students like this explanation. It helps build off of knowledge that they already have from geometry.

Law of cosine relates the two sides and a angle between them to the third side of any triangle. This is called law of cosines formula in mathematical form.

Soh-cah-toa works if the angle is greater than 0 and less than 90 degrees; cost = adj/hyp, sint = opp/hyp, cost = x/1 = x = x coordinate where terminal side of angle intersects the unit circle; sint = y/1 = y = y coordinate where the terminal side of angle intersects the unit circle; tant = sint/cost = y/