Question

An antenna has 4 guy-wires connected to the top of the antenna, and each guy-wire is anchored to the ground. A side-view of this scenario is shown.One of the guy-wires forms an angle of α=0.28 radians with the antenna and the opposing guy-wire forms an angle of β=0.39 radians with the antenna. Anchor 1 is 56 feet from the base of the antenna.How tall is the antenna? ____feet   What is the distance between anchor 2 and the base of the antenna? (Hint: you will need to use your answer to part (a).)_____ feet

Answer 1

The angle made by anchor 1 with the antenna, α=0.28 rad.

The angle made by anchor 2 with the antenna, β=0.39 rad.

The distance from the base of the antenna to anchor 1, a=56 ft.

a)

Let h be the height of the antenna.

Using trigonometric property,

`\begin{gathered} \text{tan}\alpha=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 0.28\text{ rad=}(a)/(h) \\ \tan 0.28\text{ rad}=\frac{56\text{ }}{h} \\ h=(56)/(\tan 0.28) \\ =194.75\text{ ft} \end{gathered}`

The height of the antenna is 194.75 feet.

b)

Let b be the distance from the base of the antenna to anchor 2.

We know, h=194.74 ft. Using trigonometric property,

`\begin{gathered} \tan \beta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \beta=(b)/(h) \\ b=h\tan \beta \\ =194.75ft*\tan 0.39 \\ =80.05\text{ ft} \end{gathered}`

Therefore, the distance between anchor 2 and the base of the antenna is 80.05 feet.