Question

You want to setup a pole of height 10 m vertically with the support of three ropes. Each
rope has to make an angle 30° with the pole. What should be the length of the rope?​

Answer 1

Let the pole be AB.

This implies AB = 10 m.

Let the length of rope be the hypotenuse.

This implies Rope length = AC = ?

So if we find the length of rope and multiply it by 3, we get the total rope length.

Let ∠ A = 30°

=> Cos 30° = Adjacent /Hypotenuse

=> √3 / 2 = 10 / Rope length

=> Rope length = 10 ×2 / √3

=> Rope length = 20 / √3 m

Hence the measure of one rope is 20 / √3 m.

So the measure of three ropes = 3 × 20/√3 = 34.64 m.

Hence the total length of ropes is 34.64 m.

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Answer 2

Given: The height of the pole = 10 m

Number of ropes = 3

Each rope makes an angle 30° with the pole.

To find: The length of the rope

Solution: We can understand from the question that each rope, the pole and the ground forms a right angles triangle, where the rope is the hypotenuse and the pole is the base [since angle between rope and pole = 30°).

Therefore,

cos 30° = height of pole/length of each rope

⇒ √3/2 = 10/length of each rope

⇒ length of each rope = 20/√3

⇒ length of each rope = 11.54 m

Hence, the length of the entire rope = 3 × 11.55 m = 34.65 m