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Understanding Pythagorean Theorem and Trigonometric Ratios in Right Triangles

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Discover the foundational concepts of the Pythagorean Theorem and trigonometric ratios with this comprehensive guide. Learn how to identify the sides of a right triangle (Hypotenuse, Opposite, Adjacent) and apply formulas like c² = a² + b². Understand SOH-CAH-TOA to calculate sine, cosine, and tangent, and when to use each formula effectively. The practical application of these concepts is included, along with examples of solving for x using the quadratic formula and using a clinometer for measurement. Perfect for students seeking clarity in geometry and algebra.

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Understanding Pythagorean Theorem and Trigonometric Ratios in Right Triangles

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Presentation Transcript

  1. Trig – So far we have... July 2011

  2. Pythagoras c2= a2+ b2 where c is the hypotenuse = the longest side

  3. SOH-CAH-TOA

  4. 3D Problems

  5. SOH-CAH-TOA

  6. Pythagorasc2 = a2 + b2 so c = (a2+ b2 )^0.5a2= c2 - b2so a = (c2 - b2 )^0.5 b2= c2 - a2 so b = (c2 - a2 )^0.5

  7. How to label a triangle • H = Hypotenuse, which is always opposite the right angle and always the longest side. It does not move, Pythag: H2 = O2 + A2 • O = opposite which is the side opposite the angle we are interested in. • A = Adjacent which lies between the right angle and the angle we are interested in.

  8. Which formulae do I use? Pythag or SOH-CAH-TOA

  9. Which Formulae ?

  10. Which Formulae ?

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  24. Which Formulae ?

  25. Practical measurementUsing a Clinometer

  26. 3D Problem Solving

  27. Today:Algebra recapsolve for xax2 + bx + c = 0Working on problems in the text book and work book.One group at a time measuring the classroom as per yesterday.

  28. solve for xax2 + bx + c = 0

  29. The Quadratic Formulae Proof

  30. Quad Formula fromhttp://users.rcn.com/mwhitney.massed/quadratic_formula_proof.htmlMs Allan’s Wiki:http://2011maths.wikispaces.com/NCEA+Level+1+Trig

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