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The Pythagorean Theorem

The Pythagorean Theorem. By: Ms. Kayla Van Auken 10 th Grade 02/17/2010. Objectives. In this lesson, you will learn how to…. prove the Pythagorean Theorem d emonstrate Pythagorean Identities can be used to show they are equivalent to the Pythagorean Theorem

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The Pythagorean Theorem

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  1. The Pythagorean Theorem By: Ms. Kayla Van Auken 10th Grade 02/17/2010

  2. Objectives In this lesson, you will learn how to…. • prove the Pythagorean Theorem • demonstrate Pythagorean Identities can be used to show they are equivalent to the Pythagorean Theorem • use Pythagorean Theorem to solve real world problems

  3. “University of Luxembourg, 2004”

  4. Review Quiz • Who was Pythagoras and what does the Pythagorean Theorem state? • What are the three types of right triangles? • How do we calculate sine, cosine, and tangent? • How do we calculate missing sides or angles of a triangle?

  5. Answers • Pythagoras- mathematician credited with creating the Pythagorean Theorem a2+b2=c2 • 3-4-5, 30-60-90, and 45-45-90 • SOH-CAH-TOA • sine, cosine, and tangent

  6. Review Right Triangles: • 3-4-5 Triangle • 45º-45º-90º Triangle • 30º-60º-90º Triangle • Special Right Triangles “onlinemathlearning.com , 2008”

  7. Review SOH-CAH-TOA • Sin A= Opposite / Hypotenuse • Cos A= Adjacent / Hypotenuse • Tan A= Opposite / Adjacent • SOH-CAH-TOA “Mudhar, 2007”

  8. Review Missing sides and angles use: • Sin A= a/c • Cos A= b/c • Tan A= a/b • Sin B= b/c • Cos B= b/a • Tan B= b/a • a² + b² = c² “Mudhar, 2007”

  9. Example • A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground. a) How high on the wall does the ladder reach? b) How far is the foot of the ladder from the wall? “onlinemathlearning.com , 2008”

  10. Answers a) sin 65˚= PQ/5 PQ = sin 65˚ × 5 = 4.53 m b) cos 65˚= RQ/5 RQ = cos 65˚ × 5 = 2.11 m onlinemathlearning.com (2008)

  11. History • Pythagoras • Specialties • followers / students • Group Discussion: Did he create the Pythagorean Theorem?

  12. The Pythagorean Theorem • a2+b2=c2 • Pythagorean Theorem Proof “Michaud, 2009”

  13. The Pythagorean Identities • sin²θ + cos²θ   =   1   • 1 + tan²θ   =   sec²θ   • 1 + cot²θ   =   csc ²θ Note: explanation on how to obtain on white board

  14. Real World Application Apply the Pythagorean Theorem/Identities to: • find the height of a building • calculate how far away your friend is • find the measurement of your TV • calculate the angle of the ramp on the moving truck

  15. Homework • Page 371 in your textbook problems 2-46 even • Due upon completion of projects

  16. Now • Get in small groups • Solve problems independently then share answers and processes • Think of ways to remember formulas • Quiz

  17. References onlinemathlearning.com (2008). Trigonometry Applications. Retrieved from http://www.onlinemathlearning.com/

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