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Unit 6 Lesson 3 Special Right Triangles

Unit 6 Lesson 3 Special Right Triangles. CCSS. Lesson Goals. Use the special right triangle theorems to find missing side lengths in right triangles. G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems .

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Unit 6 Lesson 3 Special Right Triangles

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  1. Unit 6 Lesson 3Special Right Triangles CCSS Lesson Goals Use the special right triangle theorems to find missing side lengths in right triangles. G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G-SRT 8.1: Derive and use the trigonometric ratios for special right triangles (30°,60°,90°and 45°,45°,90°). ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

  2. The Pythagorean Theorem is used to find • missingside lengths in right triangles. • Isosceles triangles have two congruent sides • and two congruent angles. • The acute angles of a right triangle are • complementary. Previously on Geometry Previously on Geometry y 17 x 8 b

  3. D A E F B C not in notes Definition Special Right Triangles • A right triangle with acute angles of 45o and 45o. • A right triangle with acute angles of 30o and 60o. 60o 45o 30o 45o

  4. You Try (not in notes) Find the missing angle measures. • xo 7 • xo 7

  5. You Try Find the missing side length. Leave answer in radical form. • c 2 2

  6. You Try Find the missing side length. Leave answer in radical form. • c 14 14

  7. You Try Find c. Leave answer in radical form. s • c s

  8. A C B 45o - 45o - 90o Triangle Theorem 45o s 45o s

  9. You Try Find the missing side length. Leave answer in radical form. • 30o • c • 60o 7

  10. You Try Find the missing side length. Leave answer in radical form. • 30o • 42 • 60o a

  11. You Try Find the missing side length. Leave answer in radical form. • 30o • 4 • 60o 2

  12. D E F 30o - 60o - 90o Triangle Theorem 60o 2n n 30o

  13. Example Find the value of x. 5 5 45o x

  14. Example Find the value of x. 45o 12 x

  15. Example Find the value of f and g. 60o f 4 30o g

  16. Example Find the value of m and n. 5 m 30o n 60o

  17. Example An equilateral triangle has side length 8 feet. Estimate the area. 8 ft

  18. Summary How are the special right triangle theorems related to the Pythagorean Theorem?

  19. Today’s Assignment • p. 554: 1 – 11, 13 – 19 odd, 29

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