Lesson Notes By Weeks and Term v4 - SHS 1
MEASUREMENT OF TRIANGLES
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MEASUREMENT OF TRIANGLES
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 7
Grade code: 1.2.2.LI.2
Strand code: 2
Sub-strand code: 2
Content standard code: 1.2.2.CS.1
Indicator code: 1.2.2.LI.2
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: MEASUREMENT OF TRIANGLES
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This lesson builds upon our prior knowledge of basic trigonometric ratios (SOH CAH TOA) from right-angled triangles. We will explore why certain angles (30°, 45°, and 60°) are considered "special" in mathematics. We will learn how to find the *exact* values of their sine, cosine, and tangent without using a calculator. This skill is fundamental in many fields, from architecture and engineering, where precise angles determine the stability of structures like the Adomi Bridge, to surveying land in our local communities, and even in graphic design and art.
Part 1: Redefining Trigonometric Ratios with the Unit Circle
Previously, we learned SOH CAH TOA for a right-angled triangle. Now, let's place that triangle on a Cartesian plane.
Imagine a circle centered at the origin (0, 0) with a radius *r*. Let's pick a point P(x, y) on the circle. If we draw a line from the origin to P, and then drop a perpendicular line from P to the x-axis, we form a right-angled triangle. The adjacent side has length *x*. The opposite side has length *y*. The hypotenuse is the radius *r*.
Using this, we can define our trigonometric ratios in a more general way: `sin(θ) = Opposite / Hypotenuse = y / r` `cos(θ) = Adjacent / Hypotenuse = x / r` `tan(θ) = Opposite / Adjacent = y / x`