A short-wave radio antenna is supported by two guy wires, 120 ft and 145 ft long.

Question

Each wire is attached to the top of the antenna and anchored to the ground at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 63° with the ground. How far apart are the anchor points? (Round your answer to the nearest foot.)

Answer 1

Katie

Draw a diagram.

Triangle ABD. B is the top of the antenna, A, D are the anchor points with AB < BD.

Let C be the foot of the antenna (point on AD).

Then we know AB = 120. BD = 145, BAC = 63 degrees.

You need to find AD.

Find AC, then CD and add them together.

For AC. Use cosine in the triangle ABC. (BCA is a right angle).

AC/120 = cos 63.

Then find BC using sin, BC/120 = sin 63.

Then in BCD you can find CD using Pythagoras' Theorem, as you know BC, BD and BCD is a right angle.

Mike