Question

I want this question step by step explanation pls help​

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Answer 1

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Option (D) = 12 m is correct.

step-by-step explanation:

{ Refer to the attachment for the diagram }

Let, the two poles are AB and CD

where AB = 18 m and CD = 12 m

Let, AC is the wire

Here, EB || CD thus EB = CD

So, EB = 12 m

Thus, AE = AB - EB = 18 - 12 m = 6 m

We know that, tan30° =

  ⇒

  ⇒ EC = AE √3

  ⇒ EC = 6√3

We see that, triangle ΔAEC is right angled, so by Pyathagorean Theorem, we get

  AE² + EC² = AC²

  ⇒ 6² + (6√3)² = AC²

  ⇒ AC² = 36 + 108

  ⇒ AC² = 144

  ⇒ AC² = 12²

  ⇒ AC = ± 12

Since, length cannot be negative,

AC = 12 m

∴ the length of the wire is 12 m

Answer 2

The tops of two poles of heights 18and 12 m are connected by a wire .If the wire makes an angle of measure 30 with horizontal then the length of the wire is 12 m.

According to the problem given ,

Height of the first pole = AB = 18 m

Height of the second pole = CD = 12 m

Length of the wire = AD

AE = AB - BE

= AB - CD

= 18 - 12

AE = 6 m

In ∆ AED ,

< AED = 90° ,

<ADE = 30° ( given )

Sin 30° = AE/AD

1/2 = 6/AD

AD = 6 × 2

AD = 12 m

Therefore ,

Length of the wire = AD = 12 m.

Hope it will help you.

✨Sai.