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lbvjy [14]
3 years ago
12

A utility pole is supported by two wires, one on each side, going in the opposite direction. The two wires form a 75-degree angl

e at the utility pole. if the wires are 12 meters and 16 meters long and secured to the ground, find the distance between the wires on the ground.
Mathematics
1 answer:
yuradex [85]3 years ago
7 0

Answer:

The distance between the wires on the ground ≈ 27 meters

Step-by-step explanation:

To determine:

Find the distance between the wires on the ground.

Information Fetching and Solution Steps:

  • A utility pole is supported by two wires, one on each side, going in the opposite direction.
  • The two wires form a 75-degree angle at the utility pole.
  • The wires are 12 meters and 16 meters long and secured to the ground

From the information,

  • it is clear that the wires make the hypotenuses of two right triangles.
  • It is important to determine the distance in each case of the opposite side to the 75^{0} angles.

Let the distance 1 be denoted as d_{1}

Let the distance 2 be denoted as d_{2}

So,

sin\:\left(75\right)\:\:=\:\:\:\frac{d_1}{12}\:

sin\:\left(75\right)\:\:=\:\:\:\frac{d_2}{16}\:

Finding d_{1}

sin\:\left(75\right)\:\:=\:\:\:\frac{d_1}{12}\:

sin\:\left(75\right)\cdot 12\:\:=\:\:\:d_1\:

0.96 × 12 = d_{1}

d_{1} = 11.52 meter        ∵ sin (75) = 0.96

Finding d_{2}

sin\:\left(75\right)\:\:=\:\:\:\frac{d_2}{16}\:

sin\:\left(75\right)\cdot 16\:\:=\:\:\:d_2\:

0.96 × 16 =  d_{2}

d_{2} = 15.36 meters

d_{1} +  d_{2} = 11.52 + 15.36

            = 26.88 meters ≈ 27 meters

Therefore, the distance between the wires on the ground ≈ 27 meters

Keywords: distance, sin theta

Learn more sin from brainly.com/question/10875265

#learnwithBrainly

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