SOME APPLICATIONS OF TRIGONOMETRY in 1 Shot FULL CHAPTER (Concept+PYQs) || Class 10th Boards

Introduction

This tutorial provides a comprehensive overview of the applications of trigonometry covered in the Class 10 curriculum. It includes essential concepts, practical applications, and problem-solving techniques that will help students prepare for their board exams effectively.

Step 1: Understand Trigonometric Concepts

• Familiarize yourself with the basic definitions of trigonometric ratios: sine, cosine, and tangent.
• Remember the relationships between these ratios in a right triangle:
  • Sine (sin) = Opposite side / Hypotenuse
  • Cosine (cos) = Adjacent side / Hypotenuse
  • Tangent (tan) = Opposite side / Adjacent side
• Practice identifying these sides in different right triangle scenarios.

Step 2: Learn the Line of Sight

• Understand the concept of line of sight, which is the straight line between two points.
• Recognize that the angle of elevation is the angle formed between the line of sight and the horizontal line when looking up.
• The angle of depression is formed when looking down from a horizontal line.

Step 3: Explore Angles of Elevation and Depression

• Practice calculating angles of elevation and depression using trigonometric ratios.
• Use the following formulas:
  • For finding height (h):
    • h = d × tan(θ)
  • For finding distance (d):
    • d = h / tan(θ)
• Apply these concepts in practical problems, like determining the height of a building or a tree from a distance.

Step 4: Solve the Ladder-Wall Problem

• Use trigonometry to solve problems involving a ladder leaning against a wall.
• Key steps:
  • Sketch the scenario and label the height of the wall, distance from the wall, and the length of the ladder.
  • Use the Pythagorean theorem if needed to find unknown lengths:
    • Ladder length² = Height² + Distance from wall²
• Practice with various ladder angles and lengths to reinforce your understanding.

Step 5: Analyze the Tower-Car Problem

• Understand how to apply trigonometry to problems involving towers and cars:
  • Measure the distance from the car to the base of the tower.
  • Use the angle of elevation from the car to the top of the tower to calculate the tower's height.
• Similar formulas as in Step 3 will apply.

Step 6: Tackle Case-Based Problems

• Focus on solving application-based problems that may combine multiple concepts.
• Read the problem carefully and identify knowns and unknowns.
• Break down the problem step-by-step, applying relevant trigonometric functions as needed.

Conclusion

This tutorial has covered the foundational concepts and practical applications of trigonometry relevant for Class 10 board exams. Focus on practicing these steps with various problems to strengthen your understanding. As you advance, consider utilizing additional resources such as practice sheets and group study sessions to enhance your skills further.