α, β are the horizontal angles measured at the ends of a base line AB to a hill top whose angle of elevation from station A is θ°. The height of the hill top above the trunnion axis of the theodolite station, is

ANS:D -

The correct option should be A if the horizontal angle at A and B are respectively α and β. The correct answer should be Option D

AC/Sinβ=BC/sinα=AB/sin[180-(α+β)]--------------properties of triangle.

AC=AB Sinβ / sin[180-(α+β)].

the vertical angle at A to the top of Hill is given as θ.

therefore---------H(height of hill) = AC tanθ

or H = AB sinβ tanθ/sin[180-(α+β)]