Consider an equilateral triangle with sides of length 2. All angles have measure
radians (60 degrees). If you draw a perpendicular from one vertex to the opposite side, it bisects the opposite side and bisects the angle, giving a right triangle with hypotenuse of length 2, one leg of length 1, and so, by the Pythagorean theorem, the other leg has length
. The half of the bisected angle, which is opposite the leg of length 1, has measure
(30 degrees) so that
and so
. That is a value a math student should have memorized.