The angle of depression of two post $P$ and $Q$ at a distance of $2$ meter on the same side of a road from a balloon $(B)$ vertically over the road are observed to be $\displaystyle 45^{\circ}$ and $\displaystyle 60^{\circ}$. What is the height of the balloon?

Let h be the height of the balloon and d be its horizontal distance from the closer post. Using the 60 degree angle of elevation at the closer post, tan(60) = h divided by d, so d equals h divided by sqrt(3). At the farther post, which is 2 m further away, tan(45) = h divided by (d + 2). Substituting d gives 1 = h divided by ((h divided by sqrt(3)) + 2). Solving this equation yields h = 3 + sqrt(3).

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