Review of Essential Skills:

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by P Rowell Tile Hill Wood School

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Presentation transcript:

Review of Essential Skills: Trigonometry & Proportioning

Right Angled Triangle Trigonometry Sides of a right-angle triangle: Hypotenuse: Opposite the 900 angle, the longest side in the triangle. Adjacent: Side, along with the hypotenuse, that “builds” the angle. Opposite: Side that the angle opens up to. The adjacent and opposite sides change depending on which acute angle you are referring to.

Consider ∆ABC: From A: Adjacent side = c Opposite side = a From C: Adjacent side = a Opposite side = c A B C a b c

Primary Trig Ratios Or remember: SOH CAH TOA Ratios that allow us to solve for unknown lengths / angles. hyp opp adj Or remember: SOH CAH TOA

Eg.1: Completely solve ∆ABC where B = 900, a = 5 cm and b = 10 cm.

Sine & Cosine Laws Trig laws that are designed for triangles that are non-right angle. SINE LAW: COSINE LAW: A b c C B a

Eg.2: Completely solve ∆GHI where g = 8 cm, G = 600 and H = 700. Eg.3: Completely solve ∆DEF where d = 10 cm, e = 15 cm and f = 17 cm.

Proportioning A solution method which uses comparisons instead of values to determine solutions. Very useful in situations with many unknowns.

Eg. 4: A circle has an area of 10 cm2 Eg.4: A circle has an area of 10 cm2. Determine the area of a circle with a radius that is 25% larger. Eg.5: The volume of a cone is 50 cm3. Determine the volume of a cone that is 35% taller with a radius that is 25% narrower at the base.