Heights and Distances Practice Test 1

Question : 23 of 40

Marks: +1, -0

A vertical tower stands on a horizontal plane and is surmounted by a flag staff of height 8 m. At a point on the plane, the angle of elevation of the bottom of the flag staff is 30° and that of the top of the flag staff is 45°. Find the height of the tower.

$8/{√3-1}m$
$6/{√3-1}m$
$10/{√3-1}m$
All of the above
None of these

Validate

Solution:

In ΔACD,

{8+h}/x=\tan45°⇒8+h=x

......(1)
In ΔBCD,

h/x=\tan30°⇒√3h=x

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

8+h=√3h

h=8/{√3-1}m

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