What triangles are congruent, and by what theorem?

Geometry in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

If x-1 and x+3 are the factors of x3+10x2+ax+b find a and b

Aflagpole broke in a storm. it was originally 8 1 81 feet tall. 2 8 28 feet are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground some distance away. how far away is the end of the pole from the base of the pole along the ground?