Profile
Settings
Refer your friends
Sign out
Measuring the height and distance of objects is an integral part of Mathematics and it needs certain calculations. While calculating the height of an object and its distance from another object, the “line of sight” plays a pivotal role. It refers to the visual field of a person. The “visual field” represents the area that gets covered by both eyes of a human being. But, the “line of sight” does not necessarily represent the entire “visual field” of a person, rather represents the vision of an individual along a straight line that does not face any kind of external obstruction.
Line of Sight
To understand the concept of “line of sight”, developing insights regarding both the “angle of elevation” and the “angle of depression” is required. When a human being watches an object that lies in a straight line from his sight, the movement of that person’s eye does not make any angle. But when an object is located upward, downward, or in an angular direction from the person’s eyes, in order to take a glance at that object, the person’s eyes need to make an angular movement. The angle formed as a consequence of looking at an object located in the upward direction is called the “angle of elevation”. On the other hand, to look at an object that is situated in a downward direction compared to the straight line vision of the person, the person’s eyes form an angle that is known as the “angle of depression”.
Formula for calculating “line of sight” is as follows –
Line of sight= √(2∗ height 1) +√(2∗ height 2)
Relation between the “Line of sight” and the “angle of elevation”
The “Line of sight” and the “angle of elevation” are two significant terms that are used in trigonometry. These two terms are mostly used while calculating the height and distance of an object. By calculating the height of an object, its measurement in the vertical direction is determined. On the contrary, distance calculation deals with measuring the horizontal distance of a certain point from an object. While calculating the height and distance of an object, understanding the “Line of sight” remains important as it facilitates the calculation. When a person looks up to an object that is located in an upward direction compared to the “Line of sight” of that person, the angle created due to the eye movement is called the “angle of elevation”. Therefore, without determining the “Line of sight”, performing the calculation for “angle of elevation” is not possible.
Formula for calculating the “Angle of elevation”
The “angle of elevation” is denoted by tanθ and the formula by which “Angle of elevation” is calculated is as follows-
Tanθ = Vertical distance/Horizontal distance
For example, the height of a building is 72 meters and a person is standing 8 meters away from the mentioned building. When the person is looking at the top of the concerned building, the observer’s eyes are making an “angle of elevation” which has been denoted as tanθ. To determine this angle, the height of the building which is 72 meters will be considered as the vertical measurement, and the distance between the observer and the building will be considered as the horizontal distance. Therefore, if the building height is divided by the horizontal distance, the “angle of elevation” can be determined which in this case will be tanθ = 72/8 = 9°.
Importance of calculating “Angle of elevation”
Calculating the “angle of elevation” provides a deep understanding of how an individual perceives the distance and height of larger objects like bridges, towers, buildings, etc. Different types of ratios like “sine”, “tangent”, “cosine”, etc. are utilized for measuring the “angle of elevation” but while denoting the angle, among these trigonometric ratios, only “tangent” is used. By calculating the “Angle of elevation”, the height of massive structures can be easily measured which significantly reduces the time-consuming task of manual measuring techniques. Therefore, this mathematical technique can be considered as an easy and less complicated one for measuring the height of structures like buildings and towers.
Conclusion
In mathematics, the calculation of height and distance remains an integral part. Usually, students are taught such calculations by making them understand how the height and distance of a building can be measured when an observer is looking at it. Calculating the “angle of elevation” teaches the students which angle a person needs to elevate his eyesight when looking at the top of a building. This calculation is a non-complex one as it can be simply calculated by dividing the height of a building by the distance of a person in meters while standing away from the building.
