Question

The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.

Answer 1

Consider RZ as the building, XR as the flag, and Y as the ground point from which the elevation angles are to be measured.

So, RZ = 25 m, ∠XYZ = 60°, ∠RYZ = 30°.

Now, in ΔRYZ,

`(RZ)/(YZ)` = tan 30°

⇒ `25/(YZ) = 1/sqrt(3)`

⇒ YZ = `25sqrt(3)` m

Also, in ΔXYZ,

`(XZ)/(YZ)` = tan 60°

`(XR + RZ)/(YZ) = sqrt(3)`

`(XR + 25)/(25sqrt(3)) = sqrt(3)`

XR + 25 = `25sqrt(3) xx sqrt(3)`

XR + 25 = 75

XR = 75 – 25 = 50

As a result, the flag's height is 50 metres.