At an orbital observatory, Emek and Tara had a short window to contact a research satellite. From the antenna's reference point, the satellite's projected position was 24 kilometers horizontally away and 18 kilometers above the reference level. Tara used the right triangle formed by these measurements and wrote tan θ = 18/24 = 3/4. She found that the required elevation angle was about 36.9 degrees. The antenna mount rotated automatically, with its angle modeled by A(t) = 30 sin(πt/6) + 36.9, where t was measured in minutes from the start of the communication window. Emek noticed that the mount reached 36.9 degrees whenever the sine term equaled 0. This occurred at t = 0, 6, and 12 minutes during the available window. The satellite would not clear an obstruction until after 4 minutes, so the first usable alignment was at t = 6. They waited for that orientation, activated the transmitter, and successfully established contact with the satellite.