Question

a radio antenna has the height of 27 ft. a support cable is attached to the top of the antenna making it angle 30 degrees as shown as the finger below. which measurement is the closest to x, length and feet, of the support cable?A) 31.2 ftB) 15.6 ftC) 46.8 ftD) 54.0 ft

Answer 1

EXPLANATION

Let's see the facts:

Radio antenna height= Adjacent cathetus = 27ft

Support cable attached = θ = 30°

Opposite cathetus = x = unknown

In order to find the value of x, we need to use the Pythagoras Theorem

tg θ = Opposite cathetus / Adjacent cathetus

Now, replacing terms:

tg 30° = x / 27ft

Multiplying both sides by 27:

27ft*tg30° = x

Switching:

x = 27ft * tg30° = 15.6 ft

Answer: 15.6ft is the measurement that is the closest to x