Question

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are ${45}^0$ and ${60}^0$. If the height of the tower is 150 m, find the distance between the objects.

Answer 1

The height of tower $AB=150m$

Let the first object be at $C$

The angle of depression is ${45}^{\circ }$

$\tan 45=\frac{AC}{AB}1=\frac{AC}{150}AC=150m$

So the first object is located at $150m$ apart the tower

Let the second object be at $D$

The angle of depression is ${60}^{\circ }$

$\tan 60=\frac{AD}{AB}\sqrt{3}=\frac{AD}{150}AC=150m\times \sqrt{3}$

So the second object is located at $150\sqrt{3}m$ apart the tower