MP Board · Class 10 · Mathematics · Applications of TrigonometryDefine the terms 'Line of Sight', 'Angle of Elevation', and 'Angle of Depression' with the help of a theoretical description used in the applications of trigonometry.

In the study of heights and distances which forms the core of the applications of trigonometry, several key terminologies are consistently used to set up right-angled triangles for solving practical problems. Firstly, the Line of Sight is defined as the imaginary straight line drawn from the observer's eye to a specific point on the object being viewed by the observer. When an observer is standing on the ground and looking up at an object situated at a higher level than the observer's eye level, the Angle of Elevation is formed. This angle is specifically measured between the horizontal line passing through the observer's eye and the upward inclined line of sight. Conversely, when the observer is positioned at an elevated location, such as the top of a tower or a hill, and looks down at an object situated at a lower level than the observer's eye, the Angle of Depression is formed. This angle is measured between the horizontal line passing through the observer's eye and the downward inclined line of sight. According to the geometric properties of parallel lines, the angle of depression is always numerically and geometrically equal to the angle of elevation due to alternate interior angles formed by the horizontal line and the line of sight when intersected by a transversal. Understanding these fundamental definitions allows students to accurately construct geometric diagrams, identify correct trigonometric ratios such as sine, cosine, and tangent, and systematically solve complex real-world problems involving heights and distances.