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

Drawing this out in a picture I have 3 unknowns

x1 = distance along the ground for the shorter wire

x2 = distance along the ground for the longer wire

y = height of the antenna

What I need to find the distance between the anchor points is x1+x2

I will use SOH CAH TOA to set up all these equations

I can find x1 using the following equation

cos 63 = x1/120

x1=120 cos 63

x1 = 54

I cannot find x2 directly, I only have one known part of the triangle and I need 2. So I can find y and use that to find x2.

sin 63 = y/120

y = 120 sin 63

y = 107

Now, I can use the Pythagorean Theorem to find x2

a²+b²=c²

107²+(x2)² = 145²

x2 = √145²-107²

x2 = 98

Total distance = 98+54 = 152 ft

Answer 2

Use the Law of Cosines

145² = d² + 120² - (2)(145)(d) cos 63°

Can you calculate and answer?