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: If is the inclination of the tower to the horizontal, then what is equal to?
Options
- A2+ 3 (x-y) x+y
- B2- 3 (x-y) x+y
- C2+ 3 (x+y) x-y
- D2- 3 (x+y) x-y
Correct answer
D. 2- 3 (x+y) x-y
Step-by-step solution
aligned & z= h 75^ -y= x-y 2 3 3 -1 3 +1 -y & = (x-y) 2 [ 3 -1 3+ 3 3- 3 3- 3 ]-y & = x-y 2 [ 3 3 -3-3+ 3 9-3 ]-y & =(x-y) [2 3 -3] 6 -y= 2 3 (x-y)-3(x+y) 6 & = z h = 2 3 (x-y)-3(x+y) 6 2 3 x-y & =2- 3 (x+y) x-y aligned