Question

From the top of a cliff 100 m high, the angles depression of two boats on opposite sides of cliff are 30° and 60°. The distance between the boats is ______.

Options

• 200.93 m

• 210.93 m

• 220.94 m

• 230.94 m

Answer 1

From the top of a cliff 100 m high, the angles depression of two boats on opposite sides of cliff are 30° and 60°. The distance between the boats is 230.94 m.

Explanation:

Let the horizontal distances from the cliff base to the two boats be a and b.

For angles of depression 30° and 60°,

`tan 30^circ = 1/sqrt(3)`

= `100/a` 

⇒ `a = 100sqrt(3)`

`tan 60^circ = sqrt(3)`

= `100/b` 

⇒ `b = 100/sqrt(3)`

Distance between boats = a + b

= `100(sqrt(3) + 1/sqrt(3))` 

= `400/sqrt(3)` 

= 230.94 m