Puma Grove, the world's best female golfer, is two shots away from winning another tournament. Puma's caddy stands on a marker exactly $200$ meters from the pin and determines the angle between the pin and Puma's ball is $110^\circ$. Standing close to her ball, Puma measures the angle between her caddy and the pin. After performing a calculation, she lines up her shot and swings. Her shot travels $234$ meters directly at the pin (exactly as planned) and lands perfectly next to the hole. **What was the measure of the angle Puma saw between her caddy and the pin?** *Do not round during your calculations. Round your final answer to the nearest degree.* [[☃ math-keypad 1]]$^\circ$