Question

A man standing on the deck of the ship which is 20 m above the sea-level, observes the angle of elevation of a bird as 30 and the angle of depression of its reflection in the sea as 60. Find the height of the bird.​

Answer 1

Answer:

Let

P be the position of the man standing on the deck.

QA be the sea level. 

And B be the position of the bird.

Given,

Angle of elevation of the bird from P=300

Angle of depression of the shadow of the bird =600.

Take BC=h

We have, PQ=20m=CA

∴ AR=(h+20)m

⇒CR=h+20+20=h+40

And let PC=CA=x

Now, In right △PCB

tan300=PCBC

Substituting the values,

⇒31=xh

⇒x=3h...(1)

In right △PCR

tan600=PCCG

Substituting the values,

⇒3=xh+40

Using equation (1)

⇒3hh+40=3

⇒h+40=3