Heights and Distances 10th Maths

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Heights and Distances:We shall now see how Trigonometry is used for finding the height and distances of various objects, without actually measuring them. Before going to problem, let us learn about to kinds of angles:The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.Angle of Elevation and Angle of depression:In the figure, the line AB drawn from the eye of the student top of the Minar is called the line of sight. The student is looking at the top of minar. The angle BAC, so formed by the line of sight of the horizontal, is called the angle of elevation of the top of the minar from eye of the Student.Now, consider the situation given in the beginning. The girl sitting on the balcony is looking down at a flowerpot placed on a stair of the temple. In this case, the line of sight is below the horizontal is called the angle of depression.Now, you may identify the lines of sight, and the angles so formed in the above figure are the angle of elevation or angles of depression?Problem 1:Finding the Height of Qutubminar:Let us refer to again. If you want to find the height BD of the minar without actually measuring it, what information do you need? You would need to know the following:The distance DE at which the student is standing from the foot of the minar. Let it be 28.5meters. The angle of elevation, BAC angle BAC, of the top of the minar. Let it be 450. The height AE of the student. Let it be 1.5 meters. From above coditions we can determine the height of the minar.In the figure, height of the student is CD = CB + BD.To find BC, we will use trigonometric ratios of angle A.In triangle ABC, the side BC is the opposite side in relation to known angle A.Which of the trigonometric ratios can we use? We can use the ratio has the two values that we have and the one we need to detrmine.i.e., is tanA or cotA