Lesson Notes By Weeks and Term v4 - SHS 2
MEASUREMENT OF TRIANGLES
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MEASUREMENT OF TRIANGLES
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Subject: Additional Mathematics
Class: SHS 2
Term: 2nd Term
Week: 6
Grade code: 2.2.2.LI.2
Strand code: 2
Sub-strand code: 2
Content standard code: 2.2.2.CS.1
Indicator code: 2.2.2.LI.2
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: MEASUREMENT OF TRIANGLES
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In our previous studies in mathematics, we have extensively used Pythagoras' Theorem and trigonometric ratios (SOH CAH TOA) to solve problems involving right-angled triangles. However, the world around us is not always made of perfect right angles. Think about a farmer's plot of land in the village, the route a tro-tro takes between three towns, or the structure of a roof truss. Many of these real-world shapes are non-right-angled triangles. This lesson introduces two powerful tools, the Sine Rule and the Cosine Rule, which allow us to find unknown sides and angles in *any* triangle, not just right-angled ones.
2.1. Standard Notation for Triangles
Before we begin, we must agree on a standard way to label a triangle. For any triangle, we label the vertices (corners) with capital letters (A, B, C) and the sides opposite these vertices with the corresponding lowercase letters (a, b, c). Side a is opposite Angle A. Side b is opposite Angle B. Side c is opposite Angle C.
This notation is essential for correctly using the Sine and Cosine rules. 2.2. Derivation of the Sine Rule
The Sine Rule establishes a relationship between the sides of a triangle and the sines of their opposite angles.