[138.4 m] From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the towe

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10th CBSE Maths

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

40 m

138.4 m

46.24 m

160 m

Explanation:

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, $\angle$DAB = 30°

$\angle$ABC = $\angle$DAB = 30° (because DA || BC)
tan30°=$\dfrac{AC}{BC}$
=>tan30°=$\dfrac{80}{BC}$
=>BC=$\dfrac{80}{tan30°}=\dfrac{80}{\left(\dfrac{1}{\sqrt{3}}\right)}$
=80×1.73=138.4 m
i.e., Distance of the bus from the foot of the tower = 138.4 m

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