Heights and Distances Practice Test 2

Question : 7 of 24

Marks: +1, -0

An airplane when flying at a height of 2000 meters above the ground passes vertically above another plane at an instant when the angle of elevation of two airplanes from the same point on ground are 45° and 30° respectively. How many meters the lower airplane is one than the other?

$2000({√3-1}/√3)$ m
$2000(√3/{√3-1} )$ m
$2000(√3/{√3+1} )$ m
All of the above
None of these

Validate

Solution:

In ΔACD,

2000/x=\tan45°=1⇒x=2000

In ΔBCD,

{2000-h}/x=\tan30°=1/√3

√3(2000-h)=x

......(2)
From equations (1) and (2)

2000=√3(2000-h)

h={2000(√3-1)}/√3

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