In the above figure, let AB be the tower and C and D be the two points on the ground from where A is observed. Join B, C, D. Let BC = a and BD = b. Join C, D with A. We get two right-angled triangles ABC and ABD with right angle at B. Also, the angles of elevation of the top of the tower AB from C and D are ∠ACB and ∠ADB respectively. These angles are complementary. So, We are to find the height of the tower, that is, AB.

From ∆ABD,

Again, from ∆ABC,

or,

or,

Now, multiplying we get,

or,

or,

AB = √ab

So the correct choice is (B).