1. From an aeroplane in the air and at a horizontal distance of 1050m, the angles of depression of the top and the base of a control tower at an instant are 36°and 41° respectively. calculate,  correct to the nearest metre the: (i) the height of the control tower (ii) shortest distance between the aeroplane and the base of the control tower. 
in Geometry Answers by Level 4 User (7.5k points)

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Draw a picture to help. In triangle ABC, A is the plane, B a point in the air at the same height as the plane and directly over the tower, and C is the base of the tower. Point D is on the line BD and represents the top of the tower. AB=1050m; CD is the height of the tower; angle BAC=41 deg; BAD=36 deg. BC=1050tan41; BD=1050tan36 so CD=BC-BD=1050(tan41-tan36)=149.88 or 150m to the nearest metre. The shortest distance, AC, is given by AB/AC=cos41, so AC=1050/cos41=1391m to the nearest metre.

by Top Rated User (1.2m points)

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