Lesson Notes By Weeks and Term v4 - SHS 1
MEASUREMENT
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MEASUREMENT
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Subject: Mathematics
Class: SHS 1
Term: 2nd Term
Week: 5
Grade code: 1.3.2.LI.3
Strand code: 3
Sub-strand code: 2
Content standard code: 1.3.2.CS.21
Indicator code: 1.3.2.LI.3
Theme: GEOMETRY AROUND US
Subtheme: MEASUREMENT
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This lesson introduces the practical application of trigonometry to solve real-world problems. We often see tall buildings, trees, or wide rivers and wonder about their dimensions. Trigonometry provides us with a powerful set of tools to calculate these lengths and heights indirectly, without having to physically measure them. In Ghana, this is crucial for professions like architecture (designing buildings in Accra), surveying (mapping land in the Ashanti Region), and even farming (planning irrigation on a slope). We will focus on using the three primary trigonometric ratios (sine, cosine, and tangent) to solve problems involving angles of elevation and depression.
A. Revisiting the Right-Angled Triangle
A right-angled triangle is a triangle with one angle that is exactly 90°. The sides of this triangle have special names relative to a chosen angle (other than the 90° angle), which we often call theta (θ). Hypotenuse: The longest side, always opposite the right angle. Opposite: The side directly across from the angle θ. Adjacent: The side next to the angle θ (that is not the hypotenuse).
*Remember: The Opposite and Adjacent sides depend on which angle you are focusing on!* B. The Three Primary Trigonometric Ratios (SOH CAH TOA)
These ratios relate the angles of a right-angled triangle to the lengths of its sides. The easiest way to remember them is with the mnemonic SOH CAH TOA. SOH: Sine(θ) = Opposite / Hypotenuse (`sin θ = O/H`) CAH: Cosine(θ) = Adjacent / Hypotenuse (`cos θ = A/H`) TOA: Tangent(θ) = Opposite / Adjacent (`tan θ = O/A`)