Two boats approach a light house in mid-sea from opposite directions.The Angles of elevation of the top of the light house from two boats are 60 and 45 respectively.If the distance between the two boats is 100m,find the height of hte light house.

Let the boats be at position A and B 100 m apart. The height of light house is h m and the angles of elevation of the top of light house from the two boats are and respectively.

In triangle ADC, 

In triangle BDC,

 

The height of light house is .

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