Question

Ron observes that a bird is sitting on a tree towards his east. The angle of elevation of the bird is 450. He then moves 10 metres towards south and finds the angle of elevation of the bird is 300. What is the height of the bird?

Answer 1

For better understanding the question → Refer the attachment

Let the position of Ron be C and so he faces towards east and sits in west.

Also let DB = h   and   BC = x
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In ΔABC

Tan 45° = AB/BC

           1 = 10 + h / x

   10 + h = x              ..............(1)

Also, In ΔDBC

Tan 30° = DB/BC
 
      1/√3 =  h / x

           x = h√3       ...............(2)
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From (1) and (2)

h√3 = h + 10

h√3 - h = 10

h(√3-1) = 10 

h(1.732-1) = 10

    h = 10/0.732 = 13.66 m
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Hence height of bird = 10 + 13.66

                                 = 23.66 m 
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