Multiple choice

The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

  1. 63

  2. 30

  3. 25

  4. 45

  5. None of these
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D Correct answer
Explanation

Height difference = 60 - 35 = 25. Tan(theta) = 5/9 = Height_diff / Distance. 5/9 = 25 / Distance. Distance = (25 * 9) / 5 = 45.

AI explanation

The difference in height between the two poles is 60 minus 35, which equals 25 meters. The rope connecting them forms a right-angled triangle with the horizontal distance between the poles and the vertical height difference. Using the given tangent of the angle, we have 5 divided by 9 equals 25 divided by the distance. Solving this proportion by cross-multiplication gives a distance of 45 meters.

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