From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?

Answer: Option B

Let AC be the tower and B be the position of the bus.
Then BC = the distance of the bus from the foot of the tower.
Given that height of the tower, AC = 80 m and the angle of depression, ∠DAB = 30°
∠ABC = ∠DAB = 30° (because DA || BC)
$$\begin{array}{rl}& \tan 30^{\circ }=\frac{AC}{BC}\\ & \Rightarrow \tan 30^{\circ }=\frac{80}{BC}\\ & \Rightarrow BC=\frac{80}{\tan {30}^{\circ }}\\ & =\frac{80}{\left(\frac{1}{\sqrt{3}}\right)}\\ & =80\times 1.73=138.4\text{m}\end{array}$$
i.e., Distance of the bus from the foot of the tower = 138.4 m