question_answer

John observes that the angle of elevation of first floor of building at a point A on the ground is \[{{30}^{o}}.\] The moves\[\sqrt{3}\] units towards the building to the point B and find that the angle of elevation of the second floor of building is \[{{60}^{o}}.\] If each floor has the same height, the height of seventh floor from the ground in units is

A)  5                                

B)  7

C)  21                               

D)  35

Correct Answer: C

Solution :

Let the height of each floor be x unit \[\therefore \,\,\sqrt{3}\,=AB=OA-OB\] \[\Rightarrow \,\sqrt{3}=x\cot \,{{30}^{0}}\,-2x\,\cot \,{{60}^{0}}\] \[\Rightarrow \,x=3\] Height of building = 7(3) = 21 units