Find the cube roots of 125(cos 288° + i sin 288°).

125 (cos 288 + i sin 288)   can be written as

 125 ei 288   or 125  ei (288 +360)  or 125  ei( 288+ 720)

To take the cube root of each of these, take the cube root of the 125  ( which is 5) and divide the argument of the exponential by 3   (raising to the 1/3 power)

This results in    5 ei 96    ;   5 ei 216   ;  5 ei 336     Now using DeMovrie  (Euler formula)   one gets

                       5 (cos 96 + i sin 96)  ;   5(cos 216 + i sin 216 )  ;  5 (cos 336 + i sin 336)

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)