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Chapter 8.1

Chapter 8.1. Common Core G.SRT.8 & G.SRT.4 – Use…Pythagorean Theorem to solve right triangles in applied problems. Objective – To use the Pythagorean Theorem and its converse. Chapter 8.1 Notes. Pythagorean Thm – a 2 + b 2 = c 2 Pythagorean Triple – have to be natural numbers

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Chapter 8.1

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  1. Chapter 8.1 Common CoreG.SRT.8 & G.SRT.4 – Use…Pythagorean Theorem to solve right triangles in applied problems. Objective – To use the Pythagorean Theorem and its converse.

  2. Chapter 8.1 Notes Pythagorean Thm – a2 + b2 = c2 Pythagorean Triple – have to be natural numbers 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17

  3. a2 + b2 = c2 right triangle a2 + b2⟨ c2 obtuse triangle a2 + b2⟩ c2 acute triangle

  4. Chapter 8.2 Common CoreG.SRT.8– Use…Pythagorean Theorem to solve right triangles in applied problems. Objective – to use the properties of 45-45-90 and 30-60-90 degree triangles

  5. Chapter 8.2 Notes 45° - 45 ° - 90 ° Triangles

  6. 30° - 60 ° - 90 ° Triangles

  7. Chapter 8.3 Common CoreG.SRT.8, G.MG.1, & G.SRT.7– Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Use geometric shape, their measures, and their properties to describe objects. Objective – To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles.

  8. Chapter 8.3 Notes Trigonometric Ratios SOH-CAH-TOA Sin ∠ = _______ Cos ∠ = _______ Tan ∠ = _______

  9. Trigonometric Ratios Csc∠ = _______ = _______ Sin ∠ = Sec ∠ = _______ = _______ Cos ∠ = Cot ∠ = _______ = _______ Tan ∠ =

  10. Chapter 8.4 Common CoreG.SRT.8– Use trigonometric ratios…to solve right triangles in applied problems. Objective – To use angles of elevation and depression to solve problems.

  11. Chapter 8.4 Notes Angle of Elevation Angle of Depression These angles are always made from a horizontal line

  12. Chapter 8.5 Common CoreG.SRT.11 & G.SRT.10– Understand and apply the Law of Sines…to find unknown measurements in right an non-right triangles… Objective – To apply the Law of Sines.

  13. Chapter 8.5 Notes Law of Sine C b a A c B

  14. Chapter 8.6 Common Core G.SRT.11 & G.SRT.10 – Understand and apply the Law of Cosine…to find unknown measurements in right an non-right triangles… Objective – To apply the Law of Cosine.

  15. Chapter 8.6 Notes Law of Cosine + - 2bc Cos A + - 2acCos B + - 2abCos C C b a A c B

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