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 [tex]75^{0}[/tex] angles.
Let the distance 1 be denoted as [tex]d_{1}[/tex]
Let the distance 2 be denoted as [tex]d_{2}[/tex]
So,
[tex]sin\:\left(75\right)\:\:=\:\:\:\frac{d_1}{12}\:[/tex]
[tex]sin\:\left(75\right)\:\:=\:\:\:\frac{d_2}{16}\:[/tex]
Finding [tex]d_{1}[/tex]
[tex]sin\:\left(75\right)\:\:=\:\:\:\frac{d_1}{12}\:[/tex]
[tex]sin\:\left(75\right)\cdot 12\:\:=\:\:\:d_1\:[/tex]
0.96 × 12 = [tex]d_{1}[/tex]
[tex]d_{1}[/tex] = 11.52 meter ∵ sin (75) = 0.96
Finding [tex]d_{2}[/tex]
[tex]sin\:\left(75\right)\:\:=\:\:\:\frac{d_2}{16}\:[/tex]
[tex]sin\:\left(75\right)\cdot 16\:\:=\:\:\:d_2\:[/tex]
0.96 × 16 = [tex]d_{2}[/tex]
[tex]d_{2}[/tex] = 15.36 meters
[tex]d_{1}[/tex] + [tex]d_{2}[/tex] = 11.52 + 15.36
= 26.88 meters ≈ 27 meters
Therefore, the distance between the wires on the ground ≈ 27 meters
Keywords: distance, sin theta
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