An object is obseved from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at B is twice that at A and at C three times that at A . It AB =a, BC =b , then the height of the object is

Step-by-step solution

Let ED =h, EAB = EBD =2 , ECD =3 Now, DBE = EAB + BEA 2 = + BEA BEA = = EAB AB = EB =a Similarly, EBC = In EBC , BC = EB (180^ -3 ) b = a 3 a b = 3 3 a b = 3 -4 ³ =3-4 ² 4 ² =3- a b = 3 b-a b = 3 b-a 4 b In EBD , 2 = E D E B ED = a 2 h=2 a 3 b-a 4 b , 1- 3 b-a 4 b =2 a 3 b-a 4 b b-a 4 b = a 2 b (a+b)(3 b-a)