The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π/6 and π/3 respectively. What is the height of the hill?

Concept:Angle of elevation: The term angle of elevation DENOTES the angle from the horizontal upward to an object. An observer's line of sight would be above the horizontal.Calculation:Given: height of the building = hLet BC be the height of the hill = HAnd distance between hill and building = xIn triangle ABC,tan π/3 = BC/AB = H/x√3 = H/x⇒ x = H/√3 …. (1) Now, In triangle DEC,AB = DE = x⇒ tan π/6 = CE/DE = (H – h)/x⇒ 1/√3 = (H – h)/xPut the value of x from equation 1st\(\frac{1}{{\sqrt 3 }} = {\rm{\;}}\frac{{{\rm{H}} - {\rm{h}}}}{{\left( {\frac{{\rm{H}}}{{\sqrt 3 }}} \right)}}{\rm{\;}}\)\(\RIGHTARROW \frac{1}{{\sqrt 3 }}{\rm{}} \times {\rm{}}\left( {\frac{{\rm{H}}}{{\sqrt 3 }}} \right){\rm{}} = {\rm{\;H}} - {\rm{h}}\)⇒ H /3 = H – h⇒ H = 3H – 3h⇒ 3h = 2H∴ H = 3h/2