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# Line of Sight

The line of sight is a straight line along which an observer observes an object. It is an imaginary line that stretches between observer's eye and the object that he is looking at. If the object being observed is above the horizontal, then the angle between the line of sight and the horizontal is called angle of elevation. If the object is below the horizontal, then the angle between the line of sight and the horizontal is called the angle of depression.

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## Line of Sight Definition

The line joining the eyes of the observer and the object is called the line of sight. Suppose an observer observes an bird on a tower. In the following figure, AB represents a tower and P be the position of a man who is standing on the horizontal ground watching a bird at the top of the tower. So, the line joining the eyes of the man and the bird is called the line of sight. So, PB represents the line of sight.

## Angles between Line of Sight and Horizontal

Angle of Elevation:

The object may be above or below the horizontal. If the object is above the horizontal, the angle between the line of sight and the horizontal is called the angle of elevation.

Angle of Depression:

If the object is below the horizontal, the angle between the line of sight and the horizontal is called the angle of depression.

## Horizon Line of Sight

The horizontal line is the line which is parallel to the flat ground or plane. It is perpendicular to the vertical line which is parallel to the body of an observer. The angle of depression is the downward angle formed below a horizontal line of sight with that line of sight whereas the angle of elevation is the upward angle formed above a horizontal line of sight with that line of sight.

## Line of Sight Distance

The distance between the eye of the observer and the object is called the line of sight distance. Let us see with the help of an example how to find the distance of line of sight:

### Solved Example

Question: Solve the triangle whose legs are a = 12 and b = 30.

Solution:
The right triangle ABC, $\angle$ C = 90o, AC(b) = 30 and BC(a) = 12.

Step 1:
Use the definition of the tangent to find the $\angle$ A, we have

tan A = $\frac{a}{b}$

= $\frac{12}{30}$

= 0.4

A = arc tan(0.4)

= 21.80o

Step 2:
Apply the definition of the sine function to find c.

sin A = $\frac{a}{c}$

= $\frac{12}{c}$

sin(21.80o) = $\frac{12}{c}$

0.37 = $\frac{12}{c}$

c = $\frac{12}{0.37}$

c = 32.4

The value of c is 32.4

## Line of Sight Propagation

The simplest mode of propagation of radio waves is the propagation along line of sight paths. The concept of a wave is replaced with the concept of ray. Propagation will generally be said to be in line of sight when diffraction phenomena are negligible. In contrast with scattering problems, the observed wave in light of sight propagation is always a mixture of the incident and scattered wave.

## Line of Sight Problem

Given below are some of the problems related to the line of sight.

### Solved Examples

Question 1: A person is walking on a level ground towards a building is looking towards the top of the building. Explain how the line of sight changes.
Solution:

The man starts walking from the point P towards the building OM and he is watching an object at O. As he approaches the building, the line of sight becomes steeper.

P1, P2, P3 represent the position of the man as he approaches the building.

Question 2: A tree casts a shadow 530 ft long. Find the height of the tree if the angle of elevation of the sun is 25 degree.
Solution:

Let the height of the tree be h.

By the definition of the tangent

$\frac{h}{530}$ = tan 25o

h = 530 tan 25o

= 530 * 0.46 = 243

Therefore, the height of the tree is about 243 ft.

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