MEASUREMENT OF TRIANGLES
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Subject: Additional Mathematics
Class: SHS 2
Term: 2nd Term
Week: 7
Grade code: 2.2.2.LI.3
Strand code: 2
Sub-strand code: 2
Content standard code: 2.2.2.CS.1
Indicator code: 2.2.2.LI.3
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: MEASUREMENT OF TRIANGLES
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In our previous studies, we learned how to solve for sides and angles in right-angled triangles using SOH CAH TOA and Pythagoras' theorem. However, many real-world problems involve triangles that are not right-angled. Imagine a surveyor measuring a piece of land for a new school in your community, or a fisherman navigating between two points off the coast of Takoradi. These situations often create non-right-angled triangles. Today, we will learn powerful tools—the Sine Rule and the Cosine Rule—to measure any triangle, making our mathematical skills much more applicable to the world around us.
Prerequisite Knowledge: Basic trigonometric ratios (SOH CAH TOA). Solving simple algebraic equations. Understanding of angles and bearings.
Content: A. Introduction: Beyond the Right-Angled Triangle
We know that for a right-angled triangle, we can use SOH CAH TOA. But what about a triangle like this, often called an oblique triangle?
In triangle ABC, the side opposite angle A is labelled 'a', the side opposite angle B is 'b', and the side opposite angle C is 'c'. We need new rules for these types of triangles. B. The Sine Rule