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प्रश्न
From the top of a lighthouse, 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 is 'h' m and the line joining the ships passes through the foot of the light house, show that the distance between the ship is `("h"(tan α + tan β))/(tanα tanβ)`m.
उत्तर
Let AB be the lighthouse of height h m. Let AC = x and AD = y .
In ΔCAB,
`"AB"/"AC" = tan α`
`tan α = "h"/"x"`
`"x" = "h"/tanα` ....(i)
In ΔDAB,
`"AB"/"AD" = tanβ`
`tanα = "h"/"y"`
`y = "h"/tanβ` ....(ii)
Distance between the ships = x + y
= `"h"/tanα + "h"/tanβ`
= `"h"((tanβ + tanα)/(tanα tanβ))`
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