Chapter 12: Application of Trigonometry

 

12.1: Introduction

1. Solving Right-Angled Triangles Using Trigonometrical Ratios
2. Use of Calculator

12.2: Tables of Trigonometric Ratios

1. Tables of Trigonometric Ratios
2. Problem1-Tables of Trigonometric Ratios
3. Problem2-Tables of Trigonometric Ratios
4. Problem3-Tables of Trigonometric Ratios
5. Problem4-Tables of Trigonometric Ratios

12.3: Solution of Right Triangles

1. when one Side & Angle of Elevation are Given
2. Problem-When one Side & Angle of Elevation are Given
3. Right Angles in 3-Dimensions
4. More on Right Angles in 3-Dimensions
5. Problem 1: when one Side & Angle of Elevation are Given
6. Problem 2: when one Side & Angle of Elevation are Given
7. when One Side & Angle of Depression are Given
8. Problem 1: when One Side & Angle of Depression are Given
9. Problem2-when One Side & Angle of Depression are Given
10. when Hypotenuse & Angle of Elevation are Given
11. Problem 1: when Hypotenuse & Angle of Elevation are Given
12. when Given Sides-Angle of Elevation-Depression
13. Problem 1: when Given Sides-Angle of Elevation-Depression
14. Problem 2: when Given Sides-Angle of Elevation-Depression
15. Problem3a-when Given Sides-Angle of Elevation-Depression
16. Problem3b-when Given Sides-Angle of Elevation-Depression
17. More Examples on Application of Trigonometry

12.4: (a)-Heights and Distances

1. Problem 1: when one Side & Angle of Elevation are Given
2. Problem 2: when one Side & Angle of Elevation are Given
3. Concept of Angle of Elevation & Depression
4. Problem 1: Concept of Angle of Elevation & Depression

12.5: Engineering and Heights and Distances

1. Engineering and Heights and Distances
2. More on Engineering and Heights and Distances
3. Problem1-Engineering and Heights and Distances
4. Problem2-Engineering and Heights and Distances

12.6: Oblique Triangles

1. Concept of Oblique Triangles
2. Problem-Concept of Oblique Triangles
3. The Sine Rule
4. Problem-The Sine Rule
5. Examples on Sine Rule
6. Application of the Sine Rule
7. The Cosine Rule
8. Problem1-The Cosine Rule
9. More on The Cosine Rule
10. The Law of Tangents
11. More on The Law of Tangents
12. Problem-The Law of Tangents
13. Half Angle Formulas
14. Problem-The Sine of Half the Angle Formula
15. The Cosine of Half the Angle in Terms of the Sides
16. Problem-The Cosine of Half the Angle in Terms of the Sides
17. The Tangents of Half the Angle in Terms of the Sides
18. Problem-The Tangents of Half the Angle in Terms of the Sides

12.7: Solution of Oblique Triangles

1. When Measures of One Side and Two Angles are Given
2. Problem-When Measures of One Side and Two Angles are Given
3. When Measures of Two Side and Their Included Angles are Given
4. Problem-When Measures of Two Side and Their Included Angles are Given
5. When Measures of Three Sides are Given

12.8: Area of Triangle

1. Area of Triangle
2. Area of Triangle by Measuring Three Sides
3. Problem-Area of Eqilateral Triangle With Given Sides
4. Area of Equilateral Triangle with Given Sides
5. More on Area of a Triangle with Given Sides

12.9: Circles Connected With Triangle

1. Circles Connected With Triangles
2. Problem-Circles Connected With Triangles
3. Relation Among Radius, Circum-Angle & Chord of a Circum-Circle
4. More on Relation Among Radius, Circum-Angle & Chord of a Circum-Circle
5. Problem1-Relation Among Radius, Circum-Angle & Chord of a Circum-Circ
6. Relation Among In-Radius, Perimeter & Area of Triangle
7. Problem-Relation Among In-Radius, Perimeter & Area of Triangle
8. Relation Among ex-Radius, Perimeter & Area of Triangle
9. Problem-Relation Among ex-Radius, Perimeter & Area of Triangle

12.10: Engineering and Circles Connected With Triangles

1. Engineering and Circles Connected With Triangles
2. Problem-Engineering and Circles Connected With Triangles