Answer:
θ = 18°27'
Step-by-step explanation:
As the hint says, you need to calculate CE using the triangles ΔABC and ΔBDE.
Using segment addition, CE = CB + BE. So first use trigonometry to find these segments.
First, let's find CB.
sin 22° = CB / 4.882
CB = 1.8288
Next, let's find BE.
cos 22° = AB / 4.882
AB = 4.5265
BD = AB − 1.975
BD = 2.5515
tan 48° = BE / BD
BE = 2.8337
Now we can find CE and θ.
CE = CB + BE
CE = 4.6626
cos θ = CE / 4.915
θ = 18.443°
A minute is 1/60th of a degree.
0.443° × (60 '/°) = 27'
So θ = 18°27'.
