Heights and Distances Practice Test 1

Question : 2 of 40

Marks: +1, -0

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is:

$x/{2√2}$
$x/4$
$x√2$
$x/√2$

Validate

Solution:

CD = h meter
AB = 2h meter

OB = OD = x/2

From ΔOCD,

\tanθ=h/{x/2}={2h}/x

......(i)
From ΔOAB,

\tan (90°-θ)={AB}/{BO}

⇒\cotθ={2h}/{x/2}={4h}/x

Multiplying both equations we get

\tanθ×\cotθ={2h}/x×{4h}/x

⇒x^2=8h^2

⇒h=x/{2√2}m

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