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From an aeroplane vertically over a straight horizontal road,

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From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $α$ and $β$ . Show that the height in miles of aeroplane above the road is given by
$\frac{tan α tan β}{tan α + tan β} .$

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From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be

α

and

β

. Show that the height in miles of aeroplane above the road is given by

\frac{tan α tan β}{tan α + tan β} .

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12 mins ago

Text solutionVerified

h = B D tan α = D C tan β

But

B D + D C = 1 mi l e

h (\frac{1}{tan α} + \frac{1}{tan β}) = 1

∴ h = \frac{tan α tan β}{tan α tan β}

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Question Text	From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $α$ and $β$ . Show that the height in miles of aeroplane above the road is given by $\frac{tan α tan β}{tan α + tan β} .$
Answer Type	Text solution:1
Upvotes	150

From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given bytanα +tanβ tanα tanβ ​.

Text solutionVerified

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From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $α$ and $β$ . Show that the height in miles of aeroplane above the road is given by
$\frac{tan α tan β}{tan α + tan β} .$