Question

The tops of two poles of height 18 m and 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 .....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 12 m
(b) 10 m
(c) 8 m
(d) 4 m

Answer 1

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
Option ( a ) is correct.

I hope this helps you.

: )

Answer 2

Option A is correct.

Let the legth of wire is AC.

We know the angle which is 30°.

Length of BC = height of begger pole - height of smaller pole

= 18-12

= 6 meter

Now, applying sin rule in ΔABC as shown in figure.