Question

The angle of elevation of a cloud from a point 200m above lake is 30 degrees and the angle of its reflection in the lake is 60 degrees . Find the height of the cloud above the lake

Answer 1

position of cloud = A 
200m point above the lake = B
reflection of A in lake = F
so, AE = EF
EF = 200 + m

In ΔABC,
BC = m cot 30

in ΔCFB,
CF = 200 + (200 + m)
= 400 + m
so, BC = (400 + m)cot 60

by comparing both the values of BC 
(400 + m) cot 60 = m cot 30

( 400 + m) x 1/ root 3 = m x root3
400 + m = 3m
2m = 400
m = 200

height of the cloud = AE = 200 + m = 200 + 200 = 400m

Answer 2

A is the position of the cloud  

B is the point 200 m above the lake   

And F is the reflection of A in the lake  

Now AE = EF 

EF = (2oo + m) 

Now, from triangle ABC we have,  

BC = m cot 30° --- 1 

In triangle CFB we have,  

CF = 200 + (200 + m) 

= (400 + m)  ms  

So BC = (400+m) cot 60°  --- 2 

From equation 1 and 2 we get  

(400 + m) cot 60° = m cot 30° 

(400 +m)  x 1/ root 3 = m x root 3  

400 + m = 3m  

2m = 400 

M = 200 

So the height of the cloud   = AE = 200 + m = 200 + 200 = 400 m