The angles of depression of two points from the top of the tower are $\displaystyle 30^{\circ}$ and $\displaystyle 60^{\circ}$ If the height of the tower is 30 m then find the maximum possible distance between the two points (in m)

The maximum distance occurs when the two points are on opposite sides of the tower. Let the distances from the base to the points be x and y. Using the basic trigonometric ratio for the angle of depression, tan(60 degrees) = 30 / y, so y = 30 / sqrt(3) = 10 * sqrt(3) m. Similarly, tan(30 degrees) = 30 / x, which gives x = 30 * sqrt(3) m. The maximum possible distance is the sum of these distances, 10 * sqrt(3) + 30 * sqrt(3) = 40 * sqrt(3) m.

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