Height and distance link

Height is the measurement of an object in the vertical direction and distance is the measurement of an object from a particular point in the horizontal direction. If we imagine a line connecting the point of observation to the topmost point of the object then the horizontal line, vertical line and the imaginary line will form a triangle.

Observe the figure. Consider the observer to be at point C. The height of the object is shown by line AB. The distance of the object from the observer is given by line BC. The object may or may not be perpendicular to the ground. Line AC represents the Line of Sight when the observer is observing the topmost point of the object. Angle α represents the angle of elevation and Angle β represents the angle of depression.

Using trigonometry, if we are provided with any of the two quantities that may be a side or an angle, we can calculate all the rest of the quantities. By the law of alternate angles, the angle of elevation and angle of depression are consequently equal in magnitude (α = β). Tan α is equal to the ratio of the height and distance.

You can be provided with any two of the following information:

• The distance of the object from the observer
• The height of the object
• Angle at which the observer views the topmost point of the object (angle of elevation)
• The angle at which the observer views the object when the observer is on top of a tower/building (angle of depression)