A delivery drone is hovering at a fixed point in the air. From two points on the ground in a straight line on opposite sides of the drone, the angles of elevation of the drone are 30° and 60°. If the horizontal distance between the two points is 94 m, find the vertical height at which the drone is hovering. (Take \(\sqrt3 = 1.73\))
40.655 m
Let the drone's height be h. From the 60° point, the horizontal distance to the foot of the height is \(\dfrac{h}{\tan60^\circ} = \dfrac{h}{\sqrt3}\).
From the 30° point on the opposite side, the horizontal distance is \(\dfrac{h}{\tan30^\circ} = h\sqrt3\).
Since the two points lie on opposite sides, the total distance between them is \(\dfrac{h}{\sqrt3}+h\sqrt3 = \dfrac{4h}{\sqrt3}\).
Setting this equal to 94: \(\dfrac{4h}{\sqrt3}=94 \Rightarrow h = \dfrac{94\sqrt3}{4} = 23.5\times1.73 = 40.655\).
Hence, the drone is hovering at a height of 40.655 m.
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