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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting HW Questions ( Asgs #75-#77)? Tangent Ratios Lab Work Homework / Questions Clean-up. The Tangent Ratio.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • HW Questions (Asgs #75-#77)? • Tangent Ratios • Lab Work • Homework / Questions • Clean-up

  3. 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 leg⁄adjacent leg • tan A = a/b • “the tangent of A is a/b” a b

  4. 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

  5. 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

  6. 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

  7. Tangent Review Answer: tan 18.92° = 12⁄ON tan 18.92°  0.3428 0.3428 12⁄ON ON  12⁄0.3428  35.01 • MNO is a right triangle with N = 18.92° and leg MO = 12. • Sketch the triangle and label the known parts. • Set up an equation using tan to find leg ON. M N O

  8. Velocity & Motion Q: How far should the ball move, horizontally & vertically? 4px ? 61.2° ? Problem: tan requires a leg.

  9. The Sine Function • In a right triangle, the sine of an acute angle A is the ratio of the opposite leg to the hypotenuse. • sin A = BC/AB • In the game problem, what ratio does sin 61.2° represent? B A C 61.2°

  10. Cosine • The cosine of A is defined as the ratio of the adjacent leg to the hypotenuse. • cos A = AC/AB • In the game problem, what ratiodoes cos 61.2° represent? B A C 61.2°

  11. Summary of Trig Functions • In a right triangle: • The sine of an acute angle is the opposite leg over the hypotenuse. • The cosine of an acute angle is the adjacent leg over the hypotenuse. • The tangent of an acute angle is the opposite leg over the adjacent leg. • Mnemonic: “SOH-CAH-TOA.”

  12. Lab / Homework • 50+ minutes over the weekend: • Assignments #75-80. • Proof practice • Asgs #75-76 have problems about similar right triangles. • Lab: • Work on proof write-up and portfolio.

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

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