Question

A 7m long flag staff is fixed on the top of a tower standing on the horizontal plane.from a point on the ground, the angle of elevation of the top and bottom of the flag staff are 60°and 45°respectively.find the height of the tower corre t to one place of decimal

Answer 1

Let the height of the tower be x

Express the distance in term of x  with the angle of elevation at 45°:

tan(θ) = opp/adj

tan(45) = x/distance         [ tan(45) = 1 ]

1 = x/distance

distance = x

Express the distance in term of x  with the angle of elevation at 60°:

tan(θ) = opp/adj

tan(60) = (x + 7)/distance               [ tan(60) = √3 ]

√3 = (x + 7)/distance

distance = (x + 7) / √3

Given that both distance are equal:

x = (x + 7) / √3

x√3 = x + 7

x√3 - x = 7

x(√3 - 1) =  7

x = 7/ (√3 - 1)

x = 9.6 m

Answer: The height of the tower is 9.6m