**Answer**

Let AB be the tower.

C and D be the two points with distance 4 m and 9 m from the base respectively.

A/q,

In right ΔABC,

tan *x* = AB/BC

⇒ tan *x *= AB/4

⇒ AB = 4 tan *x* ... (i)

also,

In right ΔABD,

tan (90°-*x*) = AB/BD

⇒ cot *x *= AB/9

⇒ AB = 9 cot *x * ... (ii)

Multiplying eqn (i) and (ii)

AB^{2} = 9 cot *x *× 4 tan *x*

⇒ AB^{2} = 36

⇒ AB = ± 6

**Height cannot be negative. Therefore, the height of the tower is 6 m. Hence, Proved.**