From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Let AB is building and CD is cable tower.
In ΔABD,
AB/BD = tan 45° ⇒ 7/BD = 1 ⇒ BD = 7
In ΔACE, AC = BD = 7 m
CE/AE = tan 60° ⇒ CE/7 = √3 ⇒ CE = 7√3
Therefore, CD = CE + ED = 7√3 + 7 = 7(√3 + 1)
Hence, the height of the cable tower is 7(√3 + 1) m.