Short Answer 
The golfer needs to calculate the angle ΔABC formed with the spectator using the Law of Sines. After setting up the necessary equations and calculating the angles, it is determined that ΔABC is 28.9°.
Step 1: Understanding the Problem
The golfer needs to determine the angle formed between the spectator and the hole, known as ΔABC. To find this angle, we can use the Law of Sines, which relates the lengths of sides in a triangle to the sines of its angles. This will help us solve for the unknown angle using the measurements provided in the problem.
Step 2: Applying the Law of Sines
According to the Law of Sines, we set up the equation: BC/SinΔBAC = AB/SinΔACB. By plugging in the values from the problem, we can write: 200/Sin110° = 140/SinΔACB. From this equation, we can calculate ΔACB, which is one of the angles we need to find.
Step 3: Calculating the Unknown Angle
Now that we have ΔACB, we can determine ΔABC using the formula: ΔABC = 180° РΔBAC РΔACB. Inserting the values we have, we find that ΔABC = 180° Р(110° + 41.1°), which finally gives us ΔABC = 28.9°. Therefore, the angle between the golfer, the spectator, and the hole is established as 28.9°.