Question

The angle of elevation of a cloud as seen from a point 400m above a lake is 30 degrees & the angle of depression of its reflection in the lake is 45 degrees. Find the height of the cloud above the lake.

Answer 1

             E   |
                  |
                  |
                  |
            D    ..............................  A
                  |<-------------------->|
                  |        400m            |
        400m  |                            |
              C  |______________| B
let cloud at a point E and its image at point C .an observer at point A observe that <DAE = 30 degree and <DAC = 45 degree. join the point A, E and A,C.
CD = 400m  (given)
in triangle ADC
tan 45 = CD/AD  
1 = 400/AD
AD = 400m
in triangle ADE
tan 30 = ED/AD
1/√3 = ED/400
ED = 400/√3m
height of cloud above the lake = CD+DE = (400+400/√3)m = 400(√3 + 1)/√3 m.