Two poles standing on a horizontal ground are of heights x meters...

Two poles standing on a horizontal ground are of heights

x

meters and

40

meters respectively. The line joining their tops makes an angle of

{30}^{o}

with the ground and the distance between the foot of the poles is

30\sqrt{3}

meters, then the value of

x

can be

Two poles standing on a horizontal ground are of heights x meters and 40 meters respectively. The line joining their

Options

A $20$
B $30$
C $10$
D $50$

Correct answer

C. $10$

Step-by-step solution

Two poles standing on a horizontal ground are of heights x meters and 40 meters respectively. The line joining their
Given $AB = x, CD = 40$ ~and& $∠ DBE = {30}^{o}$
In $∆ BDE$ ,
$\dfrac{DE}{BE} = tan{30}^{o}$
$DE = BEtan{30}^{o}$
\left|40 - x\right| = 30\sqrt{3} ⋅ \dfrac{1}{3} $</p><p>$ ⇒ x = 10 or 70

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