A man stands 9 m away from a flag-pole. He observes that angle of elevation of the top of the pole is 28° and the angle of depression of the bottom of the pole is 13°. Calculate the height of pole.

Let AC be the pole and D be the point where man stands.

From figure,

In △ADB,

$\Rightarrow \text{tan 28°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow 0.532 = \dfrac{AB}{BD} \\[1em] \Rightarrow AB = BD \times 0.532 \\[1em] \Rightarrow AB = 9 \times 0.532 = 4.788 \text{ m}.$

In △BDC,

$\Rightarrow \text{tan 13°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow 0.231 = \dfrac{BC}{BD} \\[1em] \Rightarrow BC = BD \times 0.231 \\[1em] \Rightarrow BC = 9 \times 0.231 = 2.079 \text{ m}.$

AC = AB + BC = 4.788 + 2.079 = 6.867 meters.

Hence, the height of pole = 6.867 meters.