Question

A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.

Answer 1

height of the flag-staff (h) = 5(√3-1)m

• Height of tower is 5m

• In triangle BCD

• tan 45° = P/B = BC/CD = 1

• BC/CD = 1

• 5/CD = 1

• CD = 5m

•In triangle ACD

• tan 60° = P/B = AC/CD = √3

• AC/CD = √3

•( 5 + h)/5 = √3

• 5 + h = 5√3

• h = 5(√3-1)m

Answer 2

Answer:

3.66 m

Step-by-step explanation:

Find the distance between the point and the tower:

Let the distance be D.

tan(45) = 5/D

D = 5/tan(45)

D = 5 m

Find the height of the tower and the flag:

Let the height be H

tan(60) = h/5

h = 5 x tan(60)

h = 5√3 m

Find the height of the flag:

Height of the flag = height of the tower and flag - height of the tower

Height of the flag =  (5√3 - 5) m

Height of the flag =3.66 m

Answer: 3.66 m