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 ).

Answer 1

The length of the flag-staff and the distance of the building from the point P is :

• Given : height of the building = 10 m, angle of elevation of the top of building = 30°, Length of flag staff = h m, angle of elevation of the top of flag staff = 45°

• Suppose distance between point P and building be x

• In ∆PQR,

tan 30° = QR / PQ = 10 / x

1/√3 = 10 / x

=> x = 10√3 m

• In ∆PQS,

tan 45° = 10+h / x = 10+h / 10√3

1 = 10+h / 10√3

10 + h = 10√3

• h = 10(√3 - 1) m

Answer 2

IN ΔABP :-

COT 30° = AP/AB

√3 =  X/10

X = 10√3 CM

SO, AP = 10√3 CM

_________

IN ΔADP :-

TAN 45° = AD/AP

  1 = 10+BD/10√3

==> 10√3 = 10+BD

==> BD = 10√3-10

==> BD = 10[√3-1]

SO, LENGHT OF FLAGSTAFF = 10[√3-1]