From the top of a light house a man observes two sinking ships at a & b at the angle of depression of 30° & 60° respectively. if the distance of the two ships is 50m. find the height of the light house. Draw appropriate figure & name it.
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Answer:
Let AB be the light house and P and Q be the position of two ships.
⇒ In △APB,tanα=
PB
AB
⇒ tanα=
PB
h
∴ PB=
tanα
h
---- ( 1 )
⇒ In △ABQ,tanβ=
BQ
AB
⇒ tanβ=
BQ
h
∴ BQ=
tanβ
h
------ ( 2 )
Now the distance between two ships PQ=PB+BQ
⇒ PQ=
tanα
h
+
tanβ
h
[ From ( 1 ) and ( 2 )]
⇒ PQ=
tanαtanβ
htanβ+htanα
=
tanαtanβ
h(tanβ+tanα)
m
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