1 / 22

GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Warm-up: Mini-Quiz Lesson: The Tangent Ratio Homework / Questions Clean-up. Mini-quiz. Take out a (half-)sheet of paper. Name/date/period at top-right corner. Title: Quiz: Special Right Triangles Quiz is on next two slides.

tessa
Download Presentation

GBK Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Warm-up: Mini-Quiz • Lesson: The Tangent Ratio • Homework / Questions • Clean-up

  3. Mini-quiz • Take out a (half-)sheet of paper. • Name/date/period at top-right corner. • Title: Quiz: Special Right Triangles • Quiz is on next two slides. • 1 minute for first slide. • 2 minutes for second slide. • Don’t write problems down.Just write the answers.

  4. Part 1: Isosceles Right Triangles(45°-45°-90° Triangles) • If AB = BC = 5, find AC. • If AB = BC = 10, find AC. • If AB = BC = 52, find AC. • If AB = BC = 9057, find AC.

  5. Part 2: 30°-60°-90° Triangles • If FE = 7, find DE and DF. • If FE = 12, find DE and DF. • If DE = 22, find FE and DF. • If DE = 120, find FE and DF.

  6. Part 1: Isosceles Right Triangles(45°-45°-90° Triangles) • If AB = BC = 5, find AC. • If AB = BC = 10, find AC. • If AB = BC = 52, find AC. • If AB = BC = 9057, find AC.

  7. Part 2: 30°-60°-90° Triangles • If FE = 7, find DE and DF. • If FE = 12, find DE and DF. • If DE = 22, find FE and DF. • If DE = 120, find FE and DF.

  8. Velocity & Motion

  9. Velocity & Motion Q: How far should the ball move, horizontally & vertically? Suppose velocity is 4 pixels/tick, and direction is 61.2° from the horizontal. 61.2°

  10. Ratios • What is the ratio of one leg to the other in • a 45°-45°-90° triangle? • a 30°-60°-90° triangle? • a 3-4-5 right triangle?

  11. Observations • Side ratios are the same for similar triangles. • Right triangles with a pair of equal acute angles are similar (by AA). • In a right triangle, an acute angle determines the triangle’s side ratios. ~

  12. The Tangent Ratio • The tangentof an acute angle of a right triangle is the ratio of the length of the opposite leg to the length of the adjacent leg. • Abbreviated: • tan A = opposite⁄adjacent • tan A = a/b • “the tangent of A is a/b” a b

  13. Tangents • Uses of the tangent ratio: • Given a and b, find tan A or tan B. • Given A, B,tan A, or tan Band either leg, find the other leg. • Given a and b, find A or B. a b

  14. Examples • a = 12 and b = 8; find tan A and tan B. • tan A = 12⁄8 = 3⁄2 • tan B = b⁄a = 8⁄12 = 2⁄3 • tan A = 20 and b = 3; find a. • tan A = a⁄b 20 = a⁄3  a = 60 • tan B = ½ and b = 4; find a. • tan B = b⁄a ½ = 4⁄a  a = 8 a b

  15. Examples – using the calculator • A = 21° and a = 20. Find b. • tan 21° = 20⁄b • tan 21°  0.384 • b  20⁄0.384  52.08 • A = 33° and b = 9. Find a. • tan 33° = a⁄9 • tan 33°  0.649 • a 9  0.649  5.84 a b

  16. Examples – inverses / finding angles • Given a = 6 and b = 5, find A. • tan A = 6⁄5 • Now what? • We need the inverse of tan: • tan-1x = X iff tan X = x. • (Assuming X is an acute angle.) • A = tan-1(6⁄5)  50.19° a b

  17. Velocity & Motion Q: How far should the ball move, horizontally & vertically? 4px ? 61.2° ?

  18. Assignments • Now: Asg #76: from Chapter 11, Lesson 4, do: • Set I Exercises 1-21, 29-34 • Set II Exercises 39-43 • Bonus: Set III • Due Thursday, 5/16 (per. 1-2)or Friday, 5/17 (per. 7). • Also for Thursday/Friday: • Read Ch. 11, Lesson 5, and take notes. • Journal #26. • Asg #77: From Chapter 11, Lesson 5, do: • Set I Exercises 1-28 • Set II Exercises 36-40 • Due Monday, 5/20.

  19. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

  20. Open Puzzle Each digit is replaced by “X” American Mathematical Monthly, April 1954. Contributed by P.L. Chessin.

  21. Overlapping Squares puzzle

  22. Polygon Inscription • A polygon is inscribed in a circle iff all its vertices are on the circle. • Using 2 colors, is it possible to color every point on a circle (note, on the circle, not in it) such that no isosceles triangle inscribed in the circle has all three vertices the same color?

More Related