Question

The angle of depression of two ships from the top of a light house are 45 and 30 degrees towards east .if the ships are 200 metres apart,find the height of the light house? And The angle of elevation of the top of a mountain at an unknown distance from the base is 30 degrees and at a distance of 10 km further off from the mountain along the same line,the angle of elevation is 15 degrees .Determine the height of the mountain.(use tan 15 degrees=0.27)

Answer 1

Let Height of light house = OC = hIn triangle OAC, we have:tan 45 = OC/OAso, OA = h                 ... (1) In triangle OBC,tan 30 = OC/OB1/ root 3 = h/OA + 200h+200 = h root 3            [Using (1)]h(root 3 - 1) = 200h = 200 / root 3 - 1By rationalisation and simplification, we get,h = 100 (root3 + 1) m