Question

From the top of a hill the angle of depression of the two consecutive kilometre stones due to east are found to be 30o and 45o.Find the height of a hill.

Answer 1

Let AB be the hill and C and D the milestones, where C is closer to B than D. Then Tan(30)= AB/BD = 1/sqrt(3). Also, Tan(45) = AB/BC =1. Let AB = x. Then BD = sqrt(3)x and BC = x. This gives CD = {sqrt(3)-1}x = 1km. This gives x = 1/{sqrt(3)-1} which can be rationalised to {sqrt(3)+1}/2