Question

A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.

• A. ${30}^o$
• B. ${60}^o$
• C. ${15}^o$
• D. ${45}^o$

Answer 1

The correct option is D ${45}^o$


From the figure, CA = 50 m
Given : AB = CA = 50 m
To find: The angle of depression $\angle DCB$

DC and AB are the horizontals.
$\angle CDB=\angle ABC=\theta$ (Alternate interior angles)
So, in $△ABC$,
$tan\theta =\frac{AC}{AB}=\frac{50}{50}=1$
We know that, $tan\theta =1,$ when, $\theta ={45}^o$
$\Rightarrow \angle ABC=\angle BCD={45}^o$
Therefore, angle of depression = ${45}^o$