In the adjoining figure, not drawn to the scale, AB is a tower and two objects C and D are located on the ground, on the same side of AB. When observed from the top A of the tower, their angles of depression are 45° and 60°. Find the distance between the two objects, if the height of the tower is 300 m. Give your answer to the nearest meter.

From figure,

∠ACB = ∠EAC = 45° (Alternate angles are equal)
∠ADB = ∠EAD = 60° (Alternate angles are equal)

Considering right angled △ABC, we get

$\Rightarrow \text{tan 45°} = \dfrac{AB}{CB} \\[1em] \Rightarrow 1 = \dfrac{300}{CB} \\[1em] \Rightarrow CB = 300$

Considering right angled △ADB, we get

$\Rightarrow \text{tan 60°} = \dfrac{AB}{DB} \\[1em] \Rightarrow \sqrt{3} = \dfrac{300}{DB} \\[1em] \Rightarrow DB = \dfrac{300}{\sqrt{3}} \\[1em] \Rightarrow DB = 173.2$

Distance between two objects (CD) = CB - DB = 300 - 173.2 = 126.8.

Rounding off to nearest meter CD = 127 m.

Hence, the distance between two objects = 127 meters.