Question

A man wishes to find the height of a flag post which stands on a horizontal plane; at a point on this plane he finds the angle of elevation of the top of the flag post tobe 45°. On walking 30 metres towards the town he findsthe corresponding angle of elevation to be 60°. Find the height of the flag post?(a) 69 m(b) 70 m(c) 71 m(d) 74 m​

Answer 1

Answer:

Step-by-step explanation:

From the figure,

Tan45 = OB/OA = h/(x + 30)

=> 1 = h/(x+30)

=> x + 30 = h

=> x = h - 30 ---- (1)

Tan60 = OB/OC = h/x

√3 = h/x

=> h = x√3 ------ (2)

Substituting value of (1) in (2)

h  = (h - 30)√3

h = h√3 - 30√3

h(√3 - 1 ) = 30√3

h = 30√3 / (√3 - 1 )

  //multiply numerator and denominator by √3 + 1

=> h = 30√3/ (√3 - 1 ) *  (√3 + 1) / (√3 + 1)

=> h = 30(3+√3) / 2 = 15(3 + √3) = 15 * (3 + 1.732) = 70.98 m ≅ 71 m.