Cai is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 21 meters from the building. The angle of elevation from his eyes to the roof ((point AA)) is 24^{\circ} ∘ , and the angle of elevation from his eyes to the top of the antenna ((point BB)) is 35^{\circ} ∘ . If his eyes are 1.69 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.