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 ${45}^o$ and ${60}^o$. If the height of the tower is $150$ m, fine the distance between the objects.

Answer 1

Given that height of the tower is $150m$

Let the two objects be placed at point C and D respectively

In $△ABC$

$\tan {60}^o=\frac{150}{BC}$

$\Rightarrow BC=\frac{150}{\sqrt{3}}=86.7m$ $(Take\sqrt{3}=1.73)$

and in $△ABD$

$\tan {45}^o=\frac{150}{BD}\Rightarrow BD=150m$

Now, Distance between objects is $CD=BD-BC=150-86.70=63.30m$