Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve problems with angles of elevation and depression in 3D.
• Apply the Sine, Cosine, and Area Rules in 3D problems.
• Create and interpret 3D diagrams accurately.
• Solve complex, multi-step trigonometry problems.
• Apply trigonometry to navigation and surveying problems.

Lesson summary

This week, we delve deeper into the fascinating world of trigonometry, focusing on applications in three dimensions and other advanced problem-solving scenarios. Building on our previous understanding of trigonometric ratios, identities, and the sine, cosine, and area rules, we will explore how these tools can be used to model and solve real-world problems involving heights, distances, and angles in three-dimensional space. This is particularly important for various fields in South Africa, such as surveying land for housing developments, designing infrastructure like bridges and buildings, and even understanding the angles of solar panels to maximize energy capture.

Lesson notes

2. 1. Angles of Elevation and Depression in 3D In a 3D problem, the angles of elevation and depression are measured from a horizontal plane. Visualising this plane is key. Imagine standing on the ground (the horizontal plane).

Angle of Elevation: The angle formed between the horizontal plane and the line of sight upwards to an object above the plane.

Angle of Depression: The angle formed between the horizontal plane and the line of sight downwards to an object below the plane.

Important: These angles are always measured from the horizontal.