ICSE Class 10 Answered
Angle of elevation of bird at B from point O is 30o . 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 60o .
Other angles relevant to this question are marked in figure .
Let us solve this question using the property of right triangle having angles 30o , 60o and 90o .
If side opposite to 30o is 1 unit , then side opposite to 60o 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 .