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Right Triangles and Trigonometry

A brief review of Pythagorean Theorem and an overview of trigonometric ratios.

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Right Triangles and Trigonometry

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  1. Right Triangles and Trigonometry “Just the facts!”

  2. Right Triangles • A right triangle is made of two legs that form the right angle. • A right triangle contains a hypotenuse, which is the longest side of the triangle • The hypotenuse is ALWAYS across from the right angle. • The sum of the angles of a right triangle equals 180 degrees. • Therefore, if one angle equals 90 degrees, the sum of the remaining two angles must equal 90 degrees, also.

  3. Pythagorean theorem • The Pythagorean Theorem describes the relationship between the lengths of the legs and the hypotenuse of a right triangle.

  4. Pythagorean theorem examples

  5. Stop! Time to think! If I told you a triangle with sides 21, 28, and 35cm was a right triangle, how would you verify my statement?  Develop an argument to convince yourself and your partner that my statement is correct. 

  6. Stop! Time to think! Illustrate how you can use the Pythagorean Theorem to find the distance between (3,6) and (6, 2) on the coordinate grid. 

  7. Right Triangles ->Trigonometric ratios • In trigonometry, there exists a special relationship between the sides of the right triangle. These are shown as the trigonometric ratios and can be used to find a missing side or angle measure of a right triangle.

  8. Trigonometric ratios

  9. Trigonometry basics • https://www.youtube.com/watch?v=F21S9Wpi0y8

  10. Stop! Time to think! • Calculate the sine, cosine, and tangent for angle A. • Calculate the sine, cosine, and tangent for angle B. • Calculate the measure of angle A. • Calculate the measure of angle B.

  11. Quick Review

  12. Resources • 1.1: Lengths of Triangle Sides Using the Pythagorean Theorem. (n.d.). Retrieved February 14, 2015, from http://www.ck12.org/book/CK-12-Trigonometry-Concepts/r2/section/1.1/ • Basic Trigonometry. (n.d.). Retrieved February 14, 2015, from https://www.youtube.com/watch?v=F21S9Wpi0y8 • Discovering Algebra Resources. (n.d.). Retrieved February 14, 2015, from http://math.kendallhunt.com/x7504.html • Learn the Pythagorean Theorem the GradeA Way. (n.d.). Retrieved February 14, 2015, from http://www.gradeamathhelp.com/pythagorean-theorem.html • PaulsOnline Notes : Calculus I - Review : Trig Functions. (n.d.). Retrieved February 14, 2015, from http://tutorial.math.lamar.edu/Classes/CalcI/TrigFcns.aspx • Right Triangle Congruence. (n.d.). Retrieved February 14, 2015, from http://www.wyzant.com/resources/lessons/math/geometry/triangles/right_triangle_congruence • Section 4: Sine And Cosine Rule. (n.d.). Retrieved February 14, 2015, from http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/sect4/index.htm

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