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