From a point P on the ground the angle of elevation of the top of a tower is `30^@` and that of the top a flagstaff fixed on the top of the tower is `60^@`. If the length of the flagstaff is `5 m,` find the height of the tower.

Explanation

The length of flagstaff AB be 5 m and P be any point on the ground. Let height of tower BC be h m.
In right `DeltaBCP`,
`tan30^(@)=(BC)/(PC)`
`rArr 1/sqrt3=h/xrArrx=hsqrt3 …(1)`
In right `DeltaACP`,
`tan60^(@)=(AC)/(PC)rArrsqrt3=(h+5)/x`
`rArr x=(h+5)/sqrt3 ...(2)`
From equations (1) and (2), we get
`hsqrt3=(h+5)/sqrt3rArr3h=h+5`
`rArr 2h=5 rArr h=2.5 m`
Hence, the height of the tower is 2.5 m.