Three points one each at the bottom of two ships and a light-house are on the same straight line. From a point at the top of the light-house just vertically above the point at the bottom, the angles of depression of the points at the bottom of the ships are 60° and 30° respectively. If the distance of the points at the bottom of the light-house and at the bottom of the first ship is 150 metres,what is the distance between the two points, one at the bottom of the light-house and the other at the bottom of the other ship? What is the height of the light-house ?
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10th
Maths
Some Applications of Trigonometry
Heights and Distances
From the top light house, t...
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Asked on December 27, 2019 by
Aahana Balaji
From the top light house, the angles of the depression of two ship on the opposite side of it are observed to be α and β. If the height of the light house be h metres and the line joining the ship passes through the foot of the light house, show that the distance between the ship is
tanαtanβ
h(tanα+tanβ)
meters.
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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
solution