The tops of two poles of height 16 m and 10 m are connected by a

Question:

The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =

(a) 26

(b) 16

(c) 12

(d) 10

Solution:

Let AB and CD be the poles such that AB = 16 m and CD = 10 m.

The given information can be represented as

Here, AC is the length of wire which is .

Also, AE = AB − BE = 16 m − 10 m = 6 m

We have to find the length of wire  .

So we use trigonometric ratios.

In triangle ACE,

$\sin C=\frac{A E}{E C}$

$\Rightarrow \sin 30^{\circ}=\frac{6}{l}$

$\Rightarrow \frac{1}{2}=\frac{6}{l}$

$\Rightarrow l=12$

Hence the correct option is $c$.

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