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Question
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 (tan ∝+tan ß))/ (tan ∝+tan ∝)`
Solution
Let h be the height of light house AC. And an angle of depression of the top of light house from two ships are ∝ and ß respectively. Let` BC=x, CD=y`,. And ∠ABC =∝, ∠ADC=ß , .
We have to find distance between the ships
We have the corresponding figure as follows
We use trigonometric ratios.
In `Δ ABC`
⇒` tan ∝ =(AC)/(BC)`
⇒` tan ∝= h/x`
⇒` x= h/ tan ∝`
Again in `Δ ADC`
⇒ `tan ß=(AC)/(CD)`
⇒` tan ß= h/y`
⇒` y=h/tan ß`
Now,
⇒ `BD=x+y`
⇒ `BD= h/tan ∝ +h/tan ß`
⇒ `BD= (h(tan∝+tan ß ))/(tan ∝ tanß)`
Hence the distance between ships is `(h(tan∝+tan ß))/(tan∝ tan ß)`
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