Question

If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is​

Answer 1

√ab

Explanation:

First start by drawing a diagram (I have attached mine below)

Complementary angles sum to 180, so we can call one angle of elevation theta, and the other one 90 - theta.

Now if we look at the 2 right angled triangles in the diagram, we can see that they are similar, because they both share the same angles.
Using this, we can say that

a/h = h/b

Cross-multiplying gives us h² = ab and hence h = √ab