Two aeroplanes are observed to be in vertical line- The angle of elevation of the upper plane is - and that of the lower is - If the height of the former be H metres- find the height of the latter plane if -60o- -45o- H-3500m-

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Standard XII

Mathematics

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Two aeroplane...

Question

Two aeroplanes are observed to be in vertical line. The angle of elevation of the upper plane is $α$ and that of the lower is $β$ . If the height of the former be $H$ metres, find the height of the latter plane if $α = 60^{o}; β = 45^{o}, H = 3500 m$ .

4742.12 m

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2020.78 m

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3975.22 m

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Solution

The correct option is B $2020.78 m$
Height of the upper plane, = 3500 m
Angle of elevation of the upper plane, $60^{\circ}$
Angle of elevation of the lower plane = $45^{\circ}$
Let the horizontal distance of the planes from the point of observation be $l$
Then, the indivisual planes, the ground make a right triangle, such that
$tan ∠$ of elevation = $\frac{h e i g h t}{H o r i z o n t a l d i s t a n c e}$
For the upper plane,
$tan 60 = \frac{3500}{l}$
$l = \frac{3500}{\sqrt{3}}$
For the lower plane,
$tan 45 = \frac{h}{l}$
$h = l = \frac{3500}{\sqrt{3}} = 2020.78$ m

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Two aeroplanes are observed to be in vertical line. The angle of elevation of the upper plane is α and that of the lower is β. If the height of the former be H metres, find the height of the latter plane if α=60o;β=45o,H=3500m.

Two aeroplanes are observed to be in vertical line. The angle of elevation of the upper plane is $α$ and that of the lower is $β$ . If the height of the former be $H$ metres, find the height of the latter plane if $α = 60^{o}; β = 45^{o}, H = 3500 m$ .