Question

a vertical tower is 40m high.A man standing at a distance from a tower knows that the consine of the angle of elevation of the top of the tower is 0.48. How far is he standing from the tower​

Answer 1

"We have, cos θ = 0.53, let distance of the man from the foot of the tower be x.

AB = 20m, BC = x, then AC = √[x2 + (20)2] = √[x2 + 400]

cos θ = BC/AC = x/√[x2 + 400]

Or, 0.53 = x/√[x2 + 400]

Or, (0.53)2 = x2/[x2 + 400] [Squaring both sides]

Or, 0.2809 = x2/[x2 + 400]

Or, x2 = 0.2809x2 + 112.36

Or, x2 – 0.2809x2 = 112.36

Or, 0.7191x2 = 112.36

Or, x2 = 112.36/0.7191 = 12.5 m