Question

If the angles of elevation of a tower from two points distant a and (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is
A. √a+b
B. √a-b
C. √ab
D.√a/b

Answer 1

If the angles of elevation of a tower from two points distant a and (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is √ab

Option C is correct.

Let AB be the height of the tower and B be the foot of the tower.

AB = h, BC  = b and BD =  a

∠ ADC = 60° and ∠ACB = 30°

In Δ ADB,

tan 60° = AB/BD

√3 = h/b

∴ h = b√3  ...........(1)

In Δ ABC,

tan 30° = AB/BC

1/√3 = h/a

∴ h = a/√3  ...........(2)

comparing (1)  and (2), we have,

h² = b√3 ×  a/√3

h² = ab

∴ h =√ ab