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A man observe that when he has walked c metres up an inclination the angular depression of an object in a horizontal plan through the foot of the slope is (alfa) and also observed that when he has walked a further discance of c metres up the slope, the depression is (Beta). prove that the inclination of the slope to the horizontal is Cot -1 (2 Cot Beta – Cot alfa) a field is in the shape of parabola bounded by a strate side of length 40 metres. C is the vertx of the parabola and it is equidestance from the two ends A and B of the straight side. A verticle pillar PQ stands at the middle point Q of the straight side. If the angle of elevation of the top of the piller from A and C be respectively (alfa) and (beta) then find the angle of elevation of the piller from the point D on the curved boundary such that angle DQA = 450 . Also find the distance of the pillar from the vertex.
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