question_answer

If the angles of depression and elevation of the top of a tower of height h from the top and bottom of a second tower are x and y respectively, then height of the second tower is

A) \[h(\cot \,y+\cot \,x)\]

B) \[h(tan\,x+tan\,y)\]

C) \[h(1+tan\,x\cot \,y)\]

D) \[h(tan\,y\cot \,x+1)\]

Correct Answer: C , D

Solution :

 Let \[PQ=H\] Then from \[\Delta \,ABP,\]                 \[AP=h\,\cot \,y\]                           ??.(i) From \[\Delta \,BMQ,\,\frac{H-h}{BM}=\tan x\] or    \[H-h=AP\,\tan x\]   [since \[AP=BM\]] From equation (i),                 \[H=h\,\cot y.\tan x\]                 \[=h[1+\tan c.\cot y]\]

Solution :