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.
(Cosines problem)

Answer 1

Answer:

The required distance is 17.34 meters.

Step-by-step explanation:

The lengths of the two wires are 12 meters and 16 meters. and the angle between the wires is 75°.

Now, we have to calculate the distance between the wires on the ground.

Therefore, we have to calculate the length of the side which is the opposite side of angle 75° of the triangle formed by the wires and the ground.

Applying the formula of properties of the triangle, if the length required is x, then

$\cos 75^{\circ} = \frac{12^{2} + 16^{2} - x^{2}}{2 \times 12 \times 16}$

⇒ 99.38 = 144 + 256 - x²

⇒ x = 17.34 meters. (Answer)