Exercise 7.2 Class 10 Math Solutions – Oblique Triangles, Sine & Cosine Laws, Punjab Board

Solved Exercise 7.2 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering Law of Sines, Law of Cosines, and calculating the area of oblique triangles under various given side and angle conditions.

This page provides complete solved solutions for Exercise 7.2 from Unit 7: Trigonometry, Class 10 Mathematics, Punjab Board (PCTB). It covers solving oblique triangles using the Law of Sines and Law of Cosines, as well as finding triangle areas under three fundamental cases: two sides and included angle (SAS), three sides using Heron's formula (SSS), and one side with two angles (ASA). All problems are solved step-by-step for Matric Part 2 students.
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Exercise Overview

Exercise 7.2 in Unit 7: Trigonometry of Class 10 Punjab Board Mathematics advances beyond right-angled trigonometry to study oblique triangles–triangles that do not contain a 90° angle. This exercise equips students with powerful trigonometric laws and area formulas to solve any non-right triangle systematically.

The exercise focuses on the Law of Sines (a / sin α = b / sin β = c / sin γ) and the Law of Cosines (a² = b² + c² - 2bc cos α), providing clear criteria for choosing the appropriate law based on given measurements (AAS, ASA, SAS, or SSS). Additionally, students master three distinct methods for finding triangle areas: the sine-included angle formula (Δ = (1/2)ab sin γ), Heron's semi-perimeter formula (Δ = √[s(s-a)(s-b)(s-c)]), and the angle-side area formula (Δ = (a² sin β sin γ) / (2 sin α)).

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), questions from Exercise 7.2 frequently appear as major 4-mark questions in Section B and multi-step computational problems in Section C. Reviewing these verified, step-by-step solutions ensures students develop computational accuracy and achieve maximum marks.

FAQs

Are these Exercise 7.2 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 7.2 oblique triangle laws for the 2026-2027 session.
What is an oblique triangle in Trigonometry?
An oblique triangle is any triangle that does not contain a right angle (90°), meaning it is either acute-angled or obtuse-angled.
What is the Law of Sines and when is it used?
The Law of Sines states that a / sin α = b / sin β = c / sin γ. It is used to solve oblique triangles when two angles and one side (AAS/ASA) or two sides and an opposite angle (SSA) are given.
What is the Law of Cosines and when is it applied?
The Law of Cosines states that a² = b² + c² - 2bc cos α (or b², c² equivalents). It is applied when two sides and the included angle (SAS) or all three sides (SSS) are given.
How do you find the area of a triangle when two sides and the included angle are given?
The area is calculated using Δ = (1/2)ab sin γ = (1/2)bc sin α = (1/2)ca sin β.
How do you calculate the area of a triangle when all three sides are known?
When three sides a, b, c are given, Heron's formula is used: Δ = √[s(s - a)(s - b)(s - c)], where semi-perimeter s = (a + b + c) / 2.
How do you calculate the area of a triangle when two angles and one side are given?
The area formula is Δ = (a² sin β sin γ) / (2 sin α) or equivalent forms using the other sides and opposite angles.
Can students read these Exercise 7.2 solutions online?
Yes, the complete solved PDF notes for Exercise 7.2 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 7.2 solutions free for students?
Yes, all Exercise 7.2 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.