Some Applications of Trigonometry | Class 10 Mathematics Notes

9.1 Heights and Distances

This section introduces the practical application of trigonometric ratios to solve real-life problems involving heights and distances. The fundamental concepts of line of sight, angle of elevation, and angle of depression are explained with the help of diagrams. The line of sight is defined as the line drawn from the eye of an observer to the point in the object viewed. When the object is above the horizontal level, the angle formed between the horizontal and the line of sight is called the angle of elevation. Conversely, when the object is below the horizontal level, the angle formed is called the angle of depression. These angles are crucial in forming right-angled triangles, which allow the use of trigonometric ratios such as sine, cosine, and tangent to calculate unknown heights or distances without direct measurement. The section also discusses the approach to find the height of an object like a minar by knowing the distance from the object, the angle of elevation, and the observer's height. Using the right triangle formed, the tangent ratio is applied to find the height of the object above the observer's eye level, which is then added to the observer's height to get the total height.

📊 Diagram: Fig. 9.1; In this figure, the line AC drawn from the eye of the student to the top of the minar is called the line of sight. The student is looking at the top of the minar. The angle BAC, so formed by the line of sight with the horizontal, is called the angle of elevation of the top of the minar from the eye of the student.

🧪 Activity: Identify lines of sight and classify angles as elevation or depression in given diagrams.

🔗 Connection: Leads to solving numerical problems using these concepts in subsequent examples.