Question

A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose 60° and 30° are the maximum and the minimum angles of elevation of the bird and that they occur when the bird is at the points P and Q respectively on its path. Let θ be the angle of elevation of the bird when it is at a point on the arc of the circle exactly midway between P and Q. Find the numerical value of tan²θ. (Assume that the observer is not inside the vertical projection of the path of the bird.)

Answer 1

Let OM = d, PU = MT = UQ = TN = TS = r

Also, let PM = RS = QN = h