Question

From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take `sqrt3` = 1.732)

Answer 1

Let AB be the flag of length hm on the building BC.

We assume that BC = 10, ∠APC = 45°, ∠BPC = 30°

Now we have to find height of flag-staff and distance of the point P from the building

The corresponding figure is as follows

In a triangle BPC,

`=> tan "P" = ("BC")/("CP")`

`=> tan 30^@ = ("BC")/("CP")`

`=> "CP"="BC"/tan30^@`

`=> 10/(1/sqrt3)`

`= 10sqrt3` m

Again in a triangle ACP

`=> tan "P" = ("AC")/"CP"`

`=> 1 = ("AC")/"CP"`

`=>` AC = CP = 10`sqrt3` m

`=>` AB + BC = CP

`=>` x = 10 = 10`sqrt3`

`=> x = 10sqrt3-10`

`=>10(sqrt3-1)`

= 10 × 0.73

 h = 7.32

Hence the length is 17.32 m and distance is 7.32 m