As observed from the top of the light house of height -h- m- the angles of depression of two ships approaching it are - and - If one ship is coming from west and the other is coming from the east- find the distance between the ships-

Let PS be #10;the lighthouse of height h meters. Let PQ=x #160; #10;and PR = y. #10; #10;In #10; #10; Δ QSP, #10; #10; tanα =SPSQ ...

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Standard XII

Mathematics

Trigonometric Ratios

As observed f...

Question

As observed from the top of the light house of height 'h' m, the angles of depression of two ships approaching it are $α$ and $β$ . If one ship is coming from west and the other is coming from the east, find the distance between the ships.

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Solution

Let PS be the lighthouse of height h meters. Let SQ=x and SR = y.
In
$Δ Q S P,$
$tan α = \frac{S P}{S Q}$
$tan α = \frac{h}{x}$
$x = \frac{h}{tan α} . . . . . . . (1)$
In
$Δ R S P,$
$tan β = \frac{S P}{S R}$
$tan β = \frac{h}{y}$
$y = \frac{h}{tan β} . . . . . . . (2)$
Distance between the ships $= x + y$
$= (\frac{h}{tan α} + \frac{h}{tan β})$
$= h (\frac{tan α + tan β}{tan α . tan β})$
The value of distance between the ships $= h (\frac{tan α + tan β}{tan α . tan β})$ or $h (cot β + cot α)$

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As observed from the top of the light house of height 'h' m, the angles of depression of two ships approaching it are α and β. If one ship is coming from west and the other is coming from the east, find the distance between the ships.

As observed from the top of the light house of height 'h' m, the angles of depression of two ships approaching it are $α$ and $β$ . If one ship is coming from west and the other is coming from the east, find the distance between the ships.