Answer:
BC = 20.225
Step-by-step explanation:
Call the point on CD where the triangle vertex is point X.
Then we have ...
BC·tan(20°) = CX
DE·tan(25°) = DX
CX +DX = AB
AB·tan(20°) = AE
AE +DE = BC
Now we can write BC in terms of itself:
BC = AE +DE = AB·tan(20°) +DE
BC = (CX +DX)·tan(20°) +DE = (BC·tan(20°) +DE·tan(25°))·tan(20°) +DE
BC(1 -tan(20°)²) = DE(1 +tan(25°)·tan(20°))
BC = DE(1 +tan(25°)·tan(20°))/(1 -tan(20°)²) . . . . where DE = 15 cm
BC ≈ 20.225 cm
