Question

A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67 degree and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole?

Answer 1

Tangent problem of opp/adj

tan 67 degrees = x/137

Find tan of 67 and multiply by 137 to find the height of the pole.

Answer 2

km;k

Answer 3

Here, I assume that the 67 degree angle is between the guy-wire and the pole, otherwise the height of the attachment point at the top of the pole will be ridiculously high: 137 ft x tan67 = 137 x 2.356 =322.7 ft (unrealistic), some giant transmission towers may reach such height, but the do not employ guy-wires, they are selp-supporting steel structures with a wide base.
so instead, I use cotangent of 67 deg or tan(90 -67)deg = tan 23 deg = ctg 67 deg = 0.425
The distance from ground of the point of attachment of guy-wire and the pole is 137 ft x 0.425 = 58.225 ft
Usually the angle between the guy-wire and the pole is 25 deg. to 45 deg. 30 degrees is very common. In some situations, because of a structure such as a street or a bridge, the angle between the pole and the guy-wire may have to be stretched, flattened (increased).