Question

A 54-foot guy wire is attached to a utility pole to provide support for tje pole. The wire forms a 60° angle with the ground. How high up the pole is a wire attached?

Answer 1

The wire is attached at a height of 27√3 or 46.76 ft. to the pole.

Explanation:

The length of the wire is 54 ft.

The angle formed between the wire and the ground is 60 degree.

Here we can use the trigonometric ratios for calculating the height of the pole.

Sin 60° = opposite/ hypotenuse

Here the hypotenuse is the wire of length 54 ft and the opposite side is the pole of height 'h'

Sin 60° = h/ 54

We know that, sin60° = (√3)/2

So,

(√3) /2 = h/ 54

(√3) (54) /2 = h

h = (√3) (54) /2

h = (√3) (27)

h= 27√3 or 46.76 ft