Chapter 9: Some Applications of Trigonometry
Concepts of Elevation and Depression
This chapter introduces practical applications of trigonometry in real-world contexts. It begins with two key ideas—angle of elevation and angle of depression. The angle of elevation is formed when the observer looks up from a horizontal line of sight, while the angle of depression is formed when the observer looks down. These angles are used to estimate heights and distances indirectly, such as calculating the height of a building, a tower, or a tree by observing the angle from a certain distance.
Using Trigonometry to Solve Problems
The method involves drawing a right triangle between the observer and the object, and then using trigonometric ratios like sine, cosine, or tangent to find unknown lengths or heights. Common scenarios include finding the length of a ladder, the height of a building, or the distance across a river. The chapter provides several worked-out examples demonstrating how to apply ratios like tanθ=oppositeadjacenttanθ=adjacentopposite to compute unknown values, depending on the information given.
Real-Life Problem Solving
Through examples involving ladders, flags, towers, shadows, and river widths, the chapter shows how trigonometry is a useful tool in practical situations where direct measurement is difficult. It also highlights the importance of drawing clear diagrams, choosing the right trigonometric ratio, and carefully interpreting results. Exercises at the end offer various challenging and engaging scenarios that reinforce understanding and application of these principles in real life.