Solution:

Consider A as the man on the deck of a ship B and CE is the cliff

AB = 16 m

Angle of elevation from the top of the cliff = 45⁰

Angle of depression at the base of the cliff = 30⁰

Take CE = h, AD = x

CD = h – 16

AD = BE = x

In right triangle CAD

tan θ = CD/AD

Substituting the values

tan 45⁰ = (h – 16)/ x

So we get

1 = (h – 16)/ x

x = h – 16 ……. (1)

In right triangle ADE

tan θ = DE/AD

Substituting the values

tan 30⁰ = 16/x

So we get

1/√3 = 16/x

x = 16√3 …… (2)

Using both the equations

h – 16 = 16 √3

h = 16√3 + 16

Taking out the common terms

h = 16 (1.732 + 1)

h = 16 (2.732)

h = 43.712 = 43.71 m

Substituting the value in equation (1)

x = h – 16

x = 43.71 – 16

x = 27.71

Here

Distance of cliff = 27.71 m

Height of cliff = 43.71 m