A telephone​ pole is 60 feet tall. A guy wire 78 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

Question

A telephone​ pole, is 60 feet tall. A guy wire 78 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

The angle between the wire and the pole is approximately ________ degrees. (round to the nearest degree)

Answer 1

Let x = angle between the wire and the pole

The height of the pole is the side adjacent to the angle. The length of the wire would be the hypotenuse. With these 2 values, cos can be used.

cos x = 60/78 Take the arccos of both sides

x = arccos (60/78)

x = 40°

Answer 2

Make a sketch.

60/78 = cos x

x = arc cos(60/78)

You do the calculation.