Aliaa and Zhang Li are tennis-playing robots capable of placing shots with superhuman precision. Aliaa is about to hit its next shot to the far corner of the court. It (Aliaa) knows that the distance between itself and Zhang Li is 520\,\text{cm} 520cm 520, start text, c, m, end text , and it knows that the angle between Zhang Li and the far corner is 53^\circ 53 ∘ 53, degrees . Similarly, Zhang Li knows that the angle between Aliaa and the far corner is 100^\circ 100 ∘ 100, degrees . What distance should Aliaa hit the ball so that it lands perfectly in the far corner of the court? Do not round during your calculations. Round your final answer to the nearest centimeter.