Question

Two posts are k metre apart and the height of one is double that of the other. If from the mid-point of the line segment joining their feet, an observer finds the angles of elevation of their tops to be complementary, then find the height of the shortest post.

Answer 1

Let AB and CD be the two posts such that AB = 2 CD. 

Let M be the mid-point of CA. 

Let ∠CMD = θ and ∠AMB = 90° – θ