we can use a unit circle, where the x coordinate is cos. we can draw the obtuse triangle, and from the highest point draw a perpendicular line to the x axis, so we have a right triangle, and we notice that the right triangle is a 30-60-90 triangle. because the hypotenuse is 1, we know that the height is 1/2, so the base, or the line that lies on the x coordinate, is $\frac{sqrt3}2$, but because the x coordinate is negative, it must be $\boxed{\frac{sqrt3}2}$
