Hi Brendan.

The easiest way is to draw a line from the corner with the large angle to the opposite side. Because this is an isosceles triangle, this line divides the triangle into two congruent right triangles. As well, this line you've drawn is the height of the original triangle.

Now you have a right triangle and you know the measure of the angle opposite the height and you know the length of the side (half the base b).

You can use a trigonometric tangent function to relate the known values to the unknown values.

Does this help?
Stephen La Rocque.