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Geometry Grades 9-12 Overview: Objectives: Materials: Procedure: For this exercise, students will learn how to use cosine, sine, and tangent of an angle to figure out the length of missing sides of a right triangle. Students will be able to: Use another method, other than the Pythagorean Theorem, to find the lengths and angles of right triangles. Use cosine, sine, and tangent of an angle to figure out the hypotenuse and length of the missing sides of a right triangle. 1. 2. 3. 4. 5. 6. 7. Paper Pencil Eraser Have the students draw 3 right triangles with a second angle and one side included. Have students exchange papers and use the sine, cosine, or tangent necessary to find the rest of the sides of the triangle. Exchange papers back to the owner. Have each student check the others work. Now have them draw 3 more right triangles but this time only including two sides of the triangle. Have the students use cosine, sine, or tangent to find the angles of the right triangle. Exchange papers back to the owner. Have each student check the others work. Now present a word problem using a right Evaluation: Standards: triangle. Ask a question like, “If a 10 foot ladder is leaned up against a wall at a 60 degree angle with the ground, how high up the wall is the top of the ladder?” 8. Go around checking answers and then go over the problem. Now, have the students raise their hands if anyone had any problems on either of the exercises. If so, go over and help the student out with his or her problem, or have him or her propose the problem to the class and see if any student can solve it. How did they do? Were they able to use cosine, sine, and tangent to find the sides and angles of the triangle? Were they able to understand and answer the word problem? G.5.4 Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of angles of right triangles. G.5.6 Solve word problems involving right triangles. Standards from: http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx Picture from: http://www.learningelectronics.net/vol_5/chpt_5/1.html