Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure

Question

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections $A$ and $B$. Tower is supported by wires from a point $O$.

Distance between the base of the tower and point $O$ is $36$ cm. From point $O$, the angle of elevation of the top of the Section $B$ is $30°$ and the angle of elevation of the top of Section $A$ is $45°$.

Based on the above information, answer the following questions:

(i) Find the length of the wire from the point $O$ to the top of Section $B$.

Accepted Answer

Step 1: In $	riangle OBP$, $\cos 30° = \frac{OP}{OB} \Rightarrow \frac{\sqrt{3}}{2} = \frac{36}{OB} \Rightarrow OB = \frac{72}{\sqrt{3}} = 24\sqrt{3}$ cm.

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