Find the height of the lighthouse, Mathematics

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Two  ships  are  sailing  in  the  sea  on  either  side  of  a  lighthouse;  the  angles  of depression of two ships as observed from the top of the lighthouse are 600  and 450 respectively. If the distance between the ships is 200(1+√3/√3)meters, find the height of the lighthouse. (Ans:200m)

1634_tea ships sails.png

Ans:    In right Δ ABC

Tan 60 = h/BC

√3 = h/BC

⇒ H = √3 BC

In right Δ ABD

Tan 45 =  h/BD

h = BD

BC + BD = 200 (1+√3/√3)

68_BC.png

h = √3 BC

= √3 (200/√3)

= 200m

∴ height of light house = 200m


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