Students can go through AP SSC 10th Class Maths Notes Chapter 12 Applications of Trigonometry to understand and remember the concepts easily.

## AP State Syllabus SSC 10th Class Maths Notes Chapter 12 Applications of Trigonometry

→ If a person is looking at an object then the imaginary line joining the object and the eye of the observer is called the line of sight or ray of view.

→ An imaginary line parallel to earth surface and passing through the point of observation is called the horizontal.

→ If the line of sight is above the horizontal then the angle between them is called “angle of elevation”.

→ If the line of sight is below the horizontal then the angle between them is called the angle of depression.

→ Useful hints to solve the problems:

- Draw a neat diagram of a right triangle or a combination of right triangles if necessary.
- Represent the data given on the triangle.
- Find the relation between known values and unknown values.
- Choose appropriate trigonometric ratio and solve for the unknown.

→ The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

→ To use this application of trigonometry, we should know the following terms.

→ The terms are Horizontal line, Line of Sight, Angle of Elevation and Angle of Depression.

→ Horizontal line: A line which is parallel to earth from observation point to object is called “horizontal line”.

→ Line of Sight (or) Ray of Vision: 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: The line of sight is above the horizontal line then angle between the line of sight and the horizontal line is called “angle of elevation”.

Note:

- If the angle of observer moves towards the perpendicular line (pole/tree/ building), then angle of elevation increases and if the observer moves away from the perpendicular line (pole/tree/building), then angle of elevation decreases.
- If height of tower is doubled and the distance between the observer and foot of the tower is also doubled, then the angle of elevation remains same.
- If the angle of elevation of sun above a tower decreases, then the length of shadow of a tower increases.

→ Angle of Depression: The line of sight is below the horizontal line then angle between the line of sight and the horizontal line is called angle of depression.

Note:

- The angle of elevation and depression are always acute angles.
- The angle of elevation of a point P as seen from a point ‘O’ is always equal to the angle of depression of ‘O’ as seen from P.

→ Points to be kept in mind:

I. Trigonometric ratios in a right triangle:

II. Trigonometric ratios of some specific angles:

→ Solving Procedure:

When we want to solve the problems of height and distances, we should consider the following :

- All the objects such as tower, trees, buildings, ships, mountains, etc. shall be considered as linear for mathematical convenience.
- The angle of elevation or angle of depression is considered with reference to the horizontal line.
- The height of the observer is neglected, if it is not given in the problem.
- To find heights and distances, we need to draw figures and with the help of these figures we can solve the problems.