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 formula Area = ½ab sin C.
• Choose the appropriate rule for a given problem.
• Solve real-world contextual problems.

Lesson summary

This week, we delve deeper into the world of trigonometry, focusing on the Sine, Cosine, and Area Rules. These rules are powerful tools that allow us to solve problems involving non-right-angled triangles, which are far more common in real-world scenarios than right-angled triangles. Think about surveying land, designing roofs, or navigating using GPS – these all involve triangles that aren't neatly right-angled. Understanding these rules will empower you to tackle these problems effectively.

Lesson notes

2.1 The Sine Rule The Sine Rule establishes a relationship between the sides of a triangle and the sines of their opposite angles.

It states that for any triangle ABC: a / sin A = b / sin B = c / sin C Where: a, b, and c are the lengths of the sides of the triangle. A, B, and C are the angles opposite those sides, respectively.

When to use the Sine Rule: The Sine Rule is useful when you know: Two angles and one side (AAS or ASA). Two sides and an angle opposite one of them (SSA - Ambiguous Case, be careful!).