Question

A 50-foot wire extends from the top of an antenna to a point 35 feet from the base of the antenna. To the nearest foot,how tall is the antenna?Antenna Height:

Answer 1

Given data:

The length of the wire is l= 50 foot.

The given base length is b= 35 feet.

The expression for the height of the antena is,

`\begin{gathered} l^2=b^2+h^2 \\ h^2=l^2-b^2 \\ h=\sqrt[]{l^2-b^2} \end{gathered}`

Substitute the given values in the above expression.

`\begin{gathered} h=\sqrt[]{(50ft)^2-(35ft)^2} \\ =\sqrt[]{1275}\text{ ft} \\ =35.707\text{ ft} \\ \approx36\text{ ft} \end{gathered}`

Thus, the height of the antena is 36 ft.