Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Apply the Sine Rule to find unknown sides and angles.
• Apply the Cosine Rule to find unknown sides and angles.
• Calculate the area of a triangle using the Area Rule.
• Choose the correct rule for a given problem.
• Solve practical, real-life problems.

Lesson summary

This week, we delve deeper into trigonometry, specifically focusing on solving two-dimensional (2D) problems using trigonometric ratios and the sine, cosine, and area rules. Building upon our understanding of right-angled triangles, we will now tackle non-right-angled triangles. This is crucial because most real-world scenarios don't neatly fit into right angles. Imagine trying to determine the height of a mountain like Table Mountain, the distance across a river, or designing a roof truss – these often require solving non-right-angled triangles. Understanding these concepts unlocks the ability to solve practical surveying, navigation, and design problems.

Lesson notes

2.1 The Sine Rule The Sine Rule is used when we have information about two angles and one side (AAS or ASA) or two sides and an angle opposite one of those sides (SSA) in a triangle. For any triangle ABC, with sides a, b, and c opposite to angles A, B, and C respectively, the Sine Rule states: ``` a/sinA = b/sinB = c/sinC ``` Why does it work? The proof involves drawing a perpendicular height from one vertex to the opposite side and using basic trigonometric ratios (sin). This shows that the ratio of a side to the sine of its opposite angle is constant for all sides and angles in the triangle.