The internal vertex angle bisector to --, the median 
to --, the altitude to --, and the internal perpendicular 
bisector of -- the base of an isosceles triangle are all 
the same line segment.  So we draw it (in green) and notice
that it divides the 30 cm base into two 15 cm parts, and 
in fact, divides the entire isosceles triangle into two 
congruent right triangles:


 
So we take just the right triangle on the left:



The angle on the left is a base angle of the original 
isosceles triangle [before we whacked it in two and threw
away the right half. :)  ] 

That angle's adjacent side is 15 and the hypotenuse
of the right triangle is 17.  Only one of the three
basic trig ratios involves both the adjacent side 
and the hypotenuse.  That is the cosine which is
adjacent/hypotenuse, so the cosine is 15/17 and
the inverse cosine of 15/17 is 28.07248694°, so the
nearest whole degree for the measure of a base angle
is 28°.

Edwin