Solution:

Consider P as the man standing on the deck of the ship which is 20 m above the sea level and B is the bird

Angle of elevation of the bird from P = 30⁰ Angle of depression from P to the shadow of the bird in the sea = 60⁰

Take BC = h

PQ = 20 m = CA

AR = (h + 20) m

CE = h + 20 + 20 = h + 40 m

PC = CA = x

In right triangle PCB

tan 30⁰ = BC/PC

Substituting the values

1/ √3 = h/x

So we get

x = √3h m ……. (1)

In right triangle PCR

tan 60⁰ = CR/PC

Substituting the values

√3 = (h + 40)/ x

Using equation (1)

(h + 40)/ √3h = √3

h + 40 = √3 × √3h = 3h

By further calculation

3h – h = 40

2h = 40

h = 40/2 = 20

From the sea level the height of the bird = 20 + h = 20 + 20 = 40 m