Exercise 7.4 Class 10 Math Solutions – Three-Figure Bearings & Applications, Punjab Board

Solved Exercise 7.4 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering three-figure bearings (0°–360°), clockwise angle measurements from North, back bearings, and navigation problem-solving using Sine and Cosine laws.

This page provides complete solved solutions for Exercise 7.4 from Unit 7: Trigonometry, Class 10 Mathematics, Punjab Board (PCTB). It covers three-figure bearings (0° to 360°), clockwise directional measurements from North, forward and back bearings, parallel North line angle geometry, and applying the Law of Sines and Law of Cosines to solve practical navigation and aviation problems for Matric Part 2 students.
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Exercise Overview

Exercise 7.4 in Unit 7: Trigonometry of Class 10 Punjab Board Mathematics focuses on three-figure bearings and their practical applications in maritime navigation, aviation, and surveying. This exercise integrates directional geometry with trigonometric problem-solving to analyze real-world travel routes and distances.

Students learn the international standard convention of three-figure bearings: measuring angles clockwise from true North using a three-digit format (from 0° to 360°). The exercise teaches how to sketch accurate directional diagrams, use parallel North lines and alternate interior angles to determine interior triangle angles, compute forward and back bearings (Back Bearing = θ ± 180°), and solve for unknown journey legs and return bearings using the Sine and Cosine rules.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), bearing problems from Exercise 7.4 frequently appear in Section C as practical application long questions. Practicing these verified, step-by-step solutions ensures students develop mastery in diagrammatic angle deduction and secure top marks in board exams.

FAQs

Are these Exercise 7.4 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 7 Exercise 7.4 three-figure bearing topics for the 2026-2027 session.
What is a three-figure bearing in Mathematics?
A three-figure bearing is a directional angle measured in a clockwise direction starting from true North (0°), always expressed with three digits (e.g., 045°, 090°, 215°).
What are the three fundamental rules for writing bearings?
1) Always measure from the North line, 2) always measure clockwise, and 3) always write using three digits (e.g., 7° is written as 007°).
What is a back bearing and how is it calculated?
A back bearing is the direction from the destination point back to the starting point. If forward bearing θ < 180°, back bearing = θ + 180°; if θ ≥ 180°, back bearing = θ - 180°.
How are the Law of Sines and Law of Cosines used in bearing problems?
Bearing angles help determine interior angles of navigation triangles formed by ship or aircraft paths; the Sine and Cosine laws are then applied to calculate unknown distances and final return bearings.
What real-world navigation disciplines use three-figure bearings?
Three-figure bearings are universally used by pilots in aviation, mariners in sea navigation, military radar operators, and land surveyors.
Are all bearing problems in Exercise 7.4 solved with complete directional diagrams?
Yes, each problem is solved with clear North line references, alternate interior angle setups, interior triangle angle calculations, and step-by-step trigonometric solutions.
Can students read these Exercise 7.4 solutions online?
Yes, the complete solved PDF notes for Exercise 7.4 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 7.4 solutions free for students?
Yes, all Exercise 7.4 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.