Question

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. if the wires are 12 meters and 16 meters long and secured to the ground, find the distance between the wires on the ground.

Answer 1

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

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