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The tops of two poles of height 30 m and 14 m are connected by a string. If the wire makes an angle of 30° with the horizontal, find the length of the wire.
- a)36 m
- b)34 m
- c)30 m
- d)32 m
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The tops of two poles of height 30 m and 14 m are connected by a strin...
Understanding the Problem
In this problem, we have two poles of different heights (30 m and 14 m) connected by a wire that makes a 30° angle with the horizontal. We need to find the length of this wire.
Step 1: Determine the Height Difference
- Height of the first pole = 30 m
- Height of the second pole = 14 m
- Height difference = 30 m - 14 m = 16 m
Step 2: Visualize the Triangle
- The wire forms the hypotenuse of a right triangle where:
- The vertical side (height difference) = 16 m
- The angle with the horizontal = 30°
Step 3: Use Trigonometric Ratios
- In a right triangle, the sine function relates the opposite side to the hypotenuse:
- sin(θ) = opposite/hypotenuse
- Here, θ = 30° and the opposite side = 16 m.
Step 4: Calculate the Length of the Wire
- Rearranging the sine formula gives us:
- hypotenuse = opposite / sin(θ)
- Plugging in the values:
- hypotenuse = 16 m / sin(30°)
- Since sin(30°) = 1/2:
- hypotenuse = 16 m / (1/2) = 16 m * 2 = 32 m
Conclusion
The length of the wire connecting the tops of the two poles is 32 m, confirming that the correct answer is option D.
In this problem, we have two poles of different heights (30 m and 14 m) connected by a wire that makes a 30° angle with the horizontal. We need to find the length of this wire.
Step 1: Determine the Height Difference
- Height of the first pole = 30 m
- Height of the second pole = 14 m
- Height difference = 30 m - 14 m = 16 m
Step 2: Visualize the Triangle
- The wire forms the hypotenuse of a right triangle where:
- The vertical side (height difference) = 16 m
- The angle with the horizontal = 30°
Step 3: Use Trigonometric Ratios
- In a right triangle, the sine function relates the opposite side to the hypotenuse:
- sin(θ) = opposite/hypotenuse
- Here, θ = 30° and the opposite side = 16 m.
Step 4: Calculate the Length of the Wire
- Rearranging the sine formula gives us:
- hypotenuse = opposite / sin(θ)
- Plugging in the values:
- hypotenuse = 16 m / sin(30°)
- Since sin(30°) = 1/2:
- hypotenuse = 16 m / (1/2) = 16 m * 2 = 32 m
Conclusion
The length of the wire connecting the tops of the two poles is 32 m, confirming that the correct answer is option D.
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Community Answer
The tops of two poles of height 30 m and 14 m are connected by a strin...
The tops of two poles of height 30 m and 14 m are connected by a string. If the wire makes an angle of 30° with the horizontal.
Calculation: Let the length of the wire be h.
Height of pole 1 = 30 m AB = 30 - 14 = 16 m
In ΔABC, Sin30° = AB/AC ⇒ 1/2 = 16/h
⇒ h = 32 m
⇒ h = 32 m
∴ The length of the wire is 32 m.
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