Question

a surveyor standing 58 M from the base of a building measures the angle to the top of the building and finds it to be 39 degrees. the surveyor then measures the angle to the top of the radio tower on the building and find that it is 48°. how tall is the radio tower .

Answer 1

First, let's calculate the height to the top of the building:

Thereby,

$\begin{gathered} \tan 39=\frac{B}{58}\rightarrow B=58\tan 39 \\ \Rightarrow B=46.97m \end{gathered}$

Now, let's calculate the height to the top of the radio tower:

This way,

$\begin{gathered} \tan 48=\frac{T}{58}\rightarrow T=58\tan 48 \\ \Rightarrow T=64.42 \end{gathered}$

Substracting both heights, we'll get that:

$64.42-46.97=17.45$

The radio tower is 17.45 m tall.