ICSE Class 10 Answered

Angle of elevation of bird at B from point O is 30^o .  Point O is 50 m above the level of lake as shwn in figure.

Reflection of bird takes place at point A on lake . Angle of depression of point A from O is 60^{o .}

Other angles relevant to this question are marked in figure .

Let us solve this question using the property of right triangle having angles 30^o , 60^o and 90^o .

If side opposite to 30^o is 1 unit , then side opposite to 60^o is √3 unit and side opposit to right angle is 2 unit as shown in figure.

In right-triangle OAE , OE = 50 m , hence OA = (100 / √3 ) m

In right-triangle OAB ,  OA = (100 / √3 ) m , hence BA = (200 / √3 ) m

In right-triangle BAD ,  BA = (200 / √3 ) m , hence BD = 100 m

Hence height of bird above lake level is 100 m .