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Q.

Which are the angles of depression from the observing positions A and C respectively of the object at E.

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a

   45 ° , 60 °  

b

   30 ° , 60 °  

c

   15 ° , 30 °   

d

   45 ° , 30 °  

answer is C.

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Detailed Solution

We need to find the angles of depression from the observing positions A and C respectively of the object at E.
Question ImageSince angle of elevation is equal to angle of depression, the angle of elevation at E for C is equal to the angle of depression at C. So, the angle of depression at C is 60 °  .
The sum of the internal angles of a triangle is 180 °   Therefore, in △ABE  ,
∠ABE+∠BAE+∠AEB= 180 °  
⇒ 90 ° + 45 ° +∠AEB= 180 °  
⇒135°+∠AEB=180°
⇒∠AEB= 45 °   The angle of elevation at E for A is equal to the angle of depression at A. So, the angle of depression at C is 45 °  .
Therefore, the angle of depression at A and C are 45 °   and 60 °   respectively.
Therefore option 3 is correct.
 
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Which are the angles of depression from the observing positions A and C respectively of the object at E.