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The angle of elevation of a bird from a point 50 m above the lake is 30(Degree) and the angle of depression of its reflection in the lake is 60(Degree). find the height of the bird above the lake. With the diagram
Asked by san.dhole121409 | 09 Feb, 2024, 12:25: AM

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 .

Answered by Thiyagarajan K | 09 Feb, 2024, 10:24: AM

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