From the top of a tower h meter high, the angle of depression of two objects, which are in line to the foot of the tower is α and β (β>α). Find the distance between the two objects.


Answer:

(cotαcotβ)h meters

Step by Step Explanation:
  1. Let AB be the tower of height h meter and x meter be the distance between the two objects C and D.
    As β>α, β will be the angle of depression of the point D and α will be the angle of depression of the point C.

    The situation given in the question is represented by the image given below.

    C A D B α β h x α β
  2. In the right-angled triangle ABD, we have tanβ=ABADtanβ=hADAD=htanβAD=h cotβ[As,cotβ=1tanβ](i)
  3. In right-angled triangle ABC, we have tanα=ABACtanα=hACAC=htanαAD+x=h cotα[ As,cotα=1tanα and AC = AD + x ](ii)
  4. Now, let us subtract eq (i) from eq (ii). (AD+x)AD=h cotαh cotβx=(cotαcotβ)h
  5. Therefore, the distance between two objects is (cotαcotβ)h meters.

You can reuse this answer
Creative Commons License
whatsapp logo
Chat with us