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A cable holds an 80-foot pole straight upright, as shown.
Based on the given information, what is the approximate length of the cable, to the nearest tenth of a foot?
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A cable holds an 80foot pole straight upright as shown Based on the given information what is the approximate length of the cable to the nearest tenth of a foot class=


Answer :

rvkacademic

Answer:

90.6 feet

Step-by-step explanation:

The three segments namely,

  • the pole (80 feet)
  • the cable
  • the line connecting the base of pole to base of cable

constitute a right triangle

We can apply the law of sines to determine the length of the cable

The law of sines says
the ratio of the length of a side of a triangle to the sine of the angle opposite is the same for all sides and angles

Hence

Length of Pole/sin 62 = Length of cable /sin 90

Given

  • Length of pole = 80 feet
  • sin 62 = 0.88294759
  • sin 90 = 1

80/0.88294759 = Length of cable/1 = Length of cable

Length of cable = 80/0.88294759 = 90.6 feet

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