Question

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

• A. 11 m
• B. 12 m
• C. 13 m
• D. 10 m

Answer 1

The Correct Option is B

To solve the problem, we need to find the length of the wire connecting the tops of two poles with different heights, where the wire makes an angle of $30^\circ$ with the horizontal.

1. Understanding the Setup:
- Height of first pole = 20 m
- Height of second pole = 14 m
- Vertical difference between the tops = $20 - 14 = 6$ m
- Angle between the wire and horizontal = $30^\circ$

2. Using Trigonometry (Sine Function):
We model the situation as a right triangle where:
- Opposite side = vertical difference = 6 m
- Hypotenuse = length of the wire (to be found)
- Angle with horizontal = $30^\circ$

Using $ \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} $, we have:

$ \sin 30^\circ = \frac{6}{\text{Length}} $

3. Solving for the Length:

$ \sin 30^\circ = \frac{1}{2} $

So, $ \frac{1}{2} = \frac{6}{\text{Length}} $

$ \text{Length} = 6 \times 2 = 12 $ m

Final Answer:
The length of the wire is $ \mathbf{12 \, \text{m}} $.