we know that
CE=CD+DE
in the right triangle EDF
cos 38°=EF/DE-----> DE=EF/cos 38°-----> DE=17/cos 38°----> DE=21.57 units
∠FDE=90-38----> 52°
∠BDC=∠FDE------> vertical angles
so
∠BDC=52°
in the right triangle BDC
cos 52°=BD/CD-------> CD=BD/cos 52°----> CD=10/cos 52°---> CD=16.24
CE=CD+DE----> CE=16.24+21.57----> CE=37.81 units
the answer is
the length of CE is 37.81 units
