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 $\mathrm{O}$.
Distance between the base of the tower and point $\mathrm{O}$ is $36\mathrm{cm}$. From point $\mathrm{O}$, the angle of elevation of the top of the Section $\mathrm{B}$ is ${30}^{\circ }$ and the angle of elevation of the top of Section $\mathrm{A}$ is ${45}^{\circ }$.
Based on the above information, answer the following questions :
(i) Find the length of the wire from the point $\mathrm{O}$ to the top of Section B.
(ii) Find the distance $\mathrm{AB}$.
OR
Find the area of $△\mathrm{OPB}$.
(iii) Find the height of the Section A from the base of the tower.