Unit 7 Class 10 Math New Book Solutions
Unit 7 Class 10 Math New Book Solutions are available here with complete step-by-step PDF solutions for all exercises of the new Punjab textbook. These notes are prepared according to the latest 2026–2027 syllabus and follow the official answer key to ensure accuracy.
Exercise Wise Solutions of Unit 7 Class 10 Math New Book
Quick Overview of Unit 7 Class 10 Math New Book Solutions
Unit 7 introduces students to practical applications of trigonometry. Instead of focusing only on trigonometric ratios and identities, this chapter shows how trigonometry can be used to solve real-life problems involving heights, distances, bearings, navigation, and three-dimensional objects.
The unit covers:
- Angles of elevation and depression.
- Bearings and navigation problems.
- Applications of sine rule and cosine rule.
- Area of triangles using trigonometry.
- Three-dimensional trigonometry.
- Distances and heights in practical situations.
- Trigonometric problems involving pyramids, prisms, cuboids, and ships.
What Is Unit 7 Class 10 Math New Book About?
Unit 7 helps students apply trigonometric concepts to real-world situations. Students learn how to determine unknown heights, distances, directions, and angles using trigonometric ratios and geometric reasoning.
The chapter begins with applications of sine rule and cosine rule in non-right angled triangles. Students then study the area formula for triangles involving trigonometric ratios. Later sections introduce bearings and navigation where directions are measured clockwise from North.
The final part of the chapter focuses on three-dimensional trigonometry. Students solve problems involving cuboids, prisms, pyramids, ships, ladders, towers, and aircraft by reducing three-dimensional situations to right triangles and applying trigonometric formulas.
Solutions of Exercise 7.1 Class 10 Math New Book
Exercise 7.1 introduces the sine rule and cosine rule for solving non-right angled triangles.
Main Topics Covered
- Sine Rule
- Cosine Rule
- Finding unknown sides
- Finding unknown angles
- Solving complete triangles
Students learn when to apply sine rule and when cosine rule provides a better approach.
Solutions of Exercise 7.2 Class 10 Math New Book
Exercise 7.2 focuses on finding the area of triangles using trigonometric formulas.
Main Topics Covered
- Area formula of triangles
- Included angle method
- Practical area problems
- Applications of sine function
Students use side lengths and included angles to calculate areas without requiring perpendicular heights.
Solutions of Exercise 7.3 Class 10 Math New Book
Exercise 7.3 introduces three-dimensional trigonometry and practical applications involving solid figures.
Main Topics Covered
- Triangular prisms
- Pyramids
- Cuboids
- Angles between lines and planes
- Heights and distances
- Real-life trigonometric applications
Many questions require students to identify right triangles hidden inside three-dimensional objects before applying trigonometric ratios.
Solutions of Exercise 7.4 Class 10 Math New Book
Exercise 7.4 introduces bearings and navigation problems.
Main Topics Covered
- Bearings
- Three-figure bearings
- Directions measured from North
- Navigation problems
- Distance and displacement problems
Students learn that bearings are always measured clockwise from North and written using three figures.
Solutions of Review Exercise 7 Class 10 Math New Book
The review exercise combines concepts from the entire chapter and prepares students for examinations.
Main Topics Covered
- MCQs
- Sine Rule
- Cosine Rule
- Area of triangles
- Bearings
- Three-dimensional trigonometry
- Practical applications
Important Formulas of Unit 7
Sine Rule
a / sin α = b / sin β = c / sin γ
Cosine Rule
a² = b² + c² − 2bc cos α
b² = a² + c² − 2ac cos β
c² = a² + b² − 2ab cos γ
Area of Triangle
Area = 1/2 ab sin C
Bearing Rule
Bearings are measured clockwise from North and written using three figures.
Angle of Elevation
Angle measured above the horizontal line.
Angle of Depression
Angle measured below the horizontal line.
Common Mistakes in Unit 7
Students often make the following mistakes:
- Using sine rule instead of cosine rule.
- Writing bearings with two figures instead of three figures.
- Measuring bearings from East or West instead of North.
- Forgetting that bearings are measured clockwise.
- Using degrees incorrectly in calculator mode.
- Mixing angles of elevation and depression.
- Using incorrect triangles in three-dimensional figures.
Related Class 10 Math Resources
- Unit 1 Class 10 Math New Book Solutions
- Unit 2 Class 10 Math New Book Solutions
- Unit 3 Class 10 Math New Book Solutions
- Unit 4 Class 10 Math New Book Solutions
- Unit 5 Class 10 Math New Book Solutions
- Unit 6 Class 10 Math New Book Solutions
Frequently Asked Questions
Is Unit 7 difficult?
Unit 7 is considered one of the more challenging chapters because it combines algebra, geometry, and trigonometry together. Regular practice makes it much easier.
Are bearings measured clockwise or anticlockwise?
Bearings are always measured clockwise from North.
Which calculator mode should be used?
The calculator should remain in Degree mode for all exercises in Unit 7.
Are these solutions according to the new book?
Yes. All solutions are prepared according to the latest Punjab Textbook Board Class 10 Mathematics book for the 2026–2027 session.
Disclaimer
These Unit 7 Class 10 Math New Book Solutions are prepared for educational purposes to help students understand mathematical concepts and methods. Students are encouraged to attempt questions themselves before consulting the solutions.
Final Words
Unit 7 is one of the most practical chapters in Class 10 Mathematics because it demonstrates how trigonometry is used in engineering, navigation, surveying, aviation, and architecture. Mastering this chapter helps students build strong problem-solving skills and prepares them for advanced mathematics in higher classes.