Question

A short-wave radio antenna is supported by two guy wires, 150 ft and 170 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 65° with the ground. How far apart are the anchor points?

Answer 1

Answer:

The anchor point is 166.86 ft apart

Explanation:

The antenna and 2 wire from traingle ABC ( figure given below). we can immediately apply the law of sines

$\frac{sinB}{b} = \frac{sinC}{c}$

$sinC = \frac{c}{b} sin B = \frac{150}{170} sin 65 = 0.79$

there are two angles for which this happens c = 52.18 or c = 127.81 degree

But 127.81 + 65 > 180 so the only valid angle for c is 52.18 degree.

that mean A = 180 - B - C = 62.82 DEGREE

THUS required distance a is by the law of sines

$\frac{sinA}{a} = \frac{sinB}{b}$

$a = b \times [\frac {sinA}{sinB} = 166.86 ft$