The tops of two poles of heights 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

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12m

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10m

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Solution

The correct option is C
12m

In triangle ABC,

$B C = y = 20 - 14 = 6 m; A C = x$

$\Rightarrow t a n 30^{\circ} = \frac{y}{x}$

$\Rightarrow \frac{1}{\sqrt{3}} = \frac{6}{x}$

$\Rightarrow x = 6 \sqrt{3}$

By applying Pythagoras Theorem, the length of the wire AB is given by

$A C^{2} + B C^{2} = A B^{2} \Rightarrow (6 \sqrt{3})^{2} + 6^{2} = A B^{2} \Rightarrow 144 = A B^{2} \Rightarrow A B = 12 m$

Thus, the length of the wire is 12 m.

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The tops of two poles of heights 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

The correct option is C 12m In triangle ABC, BC=y=20−14=6 m;AC=x ⇒tan 30∘=yx ⇒1√3=6x ⇒x=6√3 By applying Pythagoras Theorem, the length of the wire AB is given by AC2+BC2=AB2⇒(6√3)2+62=AB2⇒144=AB2⇒AB=12 m Thus, the length of the wire is 12 m.