A shortwave radio antenna is supported by two guy wires 165

A short-wave radio antenna is supported by two guy wires, 165 ft and 180 ft long. 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 67° with the ground. How far apart are the anchor points? (Round your answer to the nearest foot.) ft

Solution

x = distance of anchor point of the short wire to foot of the antenna,

y = distance of anchor point of long wire to foot of antenna,

and h = height of the antenna.
then in right angle tringle
h = 165*sin67 deg = 151.88 ft
x = 165*cos 67 deg = 64.47 ft
and by Pythagoras theorem
y = sqrt(180^2 - h^2)
y = sqrt(180^2 - 151.88^2)
y = 96.61 ft
together distance of anchor points = x + y = 64.47 + 96.61 = 161.08 ft

After rounding = 161 ft.