Two poles are 10 m and 20 m high- The line joining their tops makes an angle of 15- with the horizontal- The distance between the poles is approximately equal to

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Calculating Heights and Distances

Two poles are...

Question

Two poles are $10 m$ and $20 m$ high. The line joining their tops makes an angle of $15^{\circ}$ with the horizontal. The distance between the poles is approximately equal to

36.3 m

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37.3 m

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38.3 m

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39.3 m

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Solution

The correct option is D $37.3 m$

Let $A B$ and $C D$ are two poles

$A B = 10 m$ and $C D = 20 m$

and $∠ C A E = 15^{\circ}$

Here $C E = C D - E D$

$= 20 - 10 = 10 m$

In $△ A C E,$

$\Rightarrow tan 15^{\circ} = \frac{C E}{A E}$

$\Rightarrow A E = \frac{10}{tan 15^{\circ}}$

$= \frac{10}{2 - \sqrt{3}} = 37.3 m$

Therefore the distance between the two poles is $37.3 m$

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Two poles are 10 m and 20m high. The line joining their tops makes an angle of 15∘ with the horizontal. The distance between the poles is approximately equal to

The correct option is D 37.3 mLet AB and CD are two polesAB=10 m and CD=20 mand ∠CAE=15∘Here CE=CD−ED =20−10=10mIn △ACE,⇒tan15∘=CEAE⇒AE=10tan15∘ =102−√3=37.3 mTherefore the distance between the two poles is 37.3 m

Two poles are $10 m$ and $20 m$ high. The line joining their tops makes an angle of $15^{\circ}$ with the horizontal. The distance between the poles is approximately equal to