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Three strong cables are used to brace a 20m tall pole against movement due to the wind. Each cable is attached so that the angle of elevation to the top of the pole is 55 degrees. Find the total length of the cables.

Sagot :

sqdancefan

Answer:

  73.25 m

Step-by-step explanation:

In the right triangle formed by the pole, the ground, and the cable, the pole is the side opposite the angle of elevation, and the cable is the hypotenuse of the triangle. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Solving for the Hypotenuse, we find ...

  Hypotenuse = Opposite/Sin

  cable length = (20 m)/sin(55°) ≈ 24.4155 m

The total length of the 3 cables is ...

  3 × (24.4155 m) ≈ 73.25 m

The total length of the cables is about 73.25 meters.

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In the attached, we computed the length of a single cable for a pole 3 times as high. That will be the same length as the total we seek here.

View image sqdancefan
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