NDA2022MathematicsHeights and DistancesActual
Paragraph: There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x y) . The angles of elevation of the top of the tower from P and Q are 15^ and 75^ respectively. Question: At what height is the top of the tower above the ground level?
Options
- Ax-y 2 3
- Bx-y 4 3
- Cx-y 4
- Dx-y 2
Correct answer
A. x-y 2 3
Step-by-step solution
In A C Q 75^ = h z+y z= h 75^ -y ...(i) In A C P 15^ = h z+x z= h 15^ -x ...(ii) From (i) and (ii) aligned & h 15^ - h 75^ =x-y & h ( 3 +1 3-1 - 3 -1 3 +1 )=x-y & [ [ array l 75^ = 3 -1 3 +1 75^ = 3 +1 3 -1 array ] . & h ( 3+1+2 3 -3-1+2 3 3-1 )=x-y & h(2 3 )=x-y h= x-y 2 3 aligned