From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is h(tanα+tanβ)/tanαtanβmetres
Answers
The distance between the ships AB = h(tanα + tanβ)/tanαtanβ
Step-by-step explanation:
Given :
From the top of a light house CD ,
the angle of depression of ship A = α
the angle of depression of ship B = β
the height of the light house CD = h
distance between the ships = AB = AD + DB
From the diagram,
in triangle ADC ,
tanα = CD/AD
⇒ AD = CD/ tanα
AD = h/tanα
in triangle CDB ,
tanβ = CD/DB
⇒ DB = CD/ tanβ
DB = h/ tanβ
So,
the distance between the ships AB = AD + DB
= h/tanα + h/ tanβ
= h(tanα + tanβ)/tanαtanβ
⇒ The distance between the ships AB = h(tanα + tanβ)/tanαtanβ
Know More :
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