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Understanding Right Triangles and Trigonometry: Pythagorean Theorem & Ratios

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This chapter delves into the concepts of right triangles and trigonometry, focusing on the Pythagorean Theorem and its converse. It covers special right triangles, allowing students to practice finding the hypotenuse and missing sides in simplest radical form. The chapter also introduces trigonometric ratios—sine, cosine, and tangent—using the mnemonic SOH-CAH-TOA for easy recall. Additionally, it addresses angles of elevation and depression, providing a solid foundation for further study in geometry.

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Understanding Right Triangles and Trigonometry: Pythagorean Theorem & Ratios

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  1. Right Triangles and Trigonometry Geometry Chapter 8

  2. 8-1 The Pythagorean Theorem and its converse • We are familiar with the Pythagorean Theorem:

  3. 8-1 The Pythagorean Theorem and its converse

  4. 8-1 The Pythagorean Theorem and its converse

  5. 8-1 The Pythagorean Theorem and its converse

  6. 8-1 The Pythagorean Theorem and its converse

  7. 8-1 The Pythagorean Theorem and its converse

  8. 8-1 The Pythagorean Theorem and its converse

  9. 8-2 Special Right Triangles • For each triangle, use the Pythagorean theorem to find the length of the hypotenuse. Leave the answer in simplest radical form. 2 4 2 5 4 5

  10. 8-2 Special Right Triangles

  11. 8-2 Special Right Triangles

  12. 8-2 Special Right Triangles

  13. 8-2 Special Right Triangles

  14. 8-2 Special Right Triangles

  15. 8-2 Special Right Triangles • solve for the missing sides – leave you answer in radical form.

  16. 8-2 Special Right Triangles • Homework: 420 (1-25) odd • 428 (1-15) odd

  17. 8-3 The Tangent Ratio • Warm Up

  18. 8-3 The Tangent Ratio • For each pair of complementary angles ∠A and ∠B, there is a family of similar right triangles. • In each family the ratio: • is constant no matter the size of ∆ABC

  19. 8-3 The Tangent Ratio • This trigonometric ratio is called the tangent ratio.

  20. 8-3 The Tangent Ratio

  21. 8-3 The Tangent Ratio

  22. 8-3 The Tangent Ratio

  23. 8-4 The Sine and Cosine Ratios

  24. 8-4 The Sine and Cosine Ratios

  25. 8-4 The Sine and Cosine Ratios • One way to remember which ratio corresponds to each trig function is to remember the word: SOH-CAH-TOA • SOH: sine opposite over hypotenuse • CAH: cosine adjacent over hypotenuse • TOA: tangent opposite over adjacent

  26. 8-4 The Sine and Cosine Ratios

  27. 8-4 The Sine and Cosine Ratios

  28. 8-5 Angles of Elevation and Angles of Depression

  29. 8-5 Angles of Elevation and Angles of Depression

  30. 8-5 Angles of Elevation and Angles of Depression

  31. 8-5 Angles of Elevation and Angles of Depression

  32. 8-5 Angles of Elevation and Angles of Depression • homework • page 441 (1-16) all • page 447 (1-14) all • Chapter 8 test next week Tuesday/Wednesday

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