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Mr. Wolf Tuesday 12/9/08 Geometry Grades 10-12 Unit 7: Right Triangles Review Unit 7 Materials and Resources: Warm-up (1 per student) Unit 7 Study Guide sheet (1 per student) Unit 7 Review Bingo sheet (1 per student) Exit Ticket (1 per student) PA Standards Addressed: Instructional Objectives: Students will be able to review material from Unit 7 by completing a review activity. Time 10 min 1 min 1 min 25 min Activity Warm-up Agenda Homework Check Review Homework 50 min Review Unit 7 1 min 5 min Agenda Conclusion Homework: Online Quiz #12 Lesson Reflection: Description Pass out the Warm-up and review solutions. Review the goals for the day. Spot-check and review solutions Present the HW solutions and answer any questions. Modeling: Guiding: Independent Practice: Assessment: Modifications: Students with special needs… Advanced students… Revisit goals and identify whether they were met. Pass out the Exit Ticket and collect at the bell. Geometry Fall 2008 Name: ________________________ Warm-up In Greek mythology, Sisyphus was condemned to an eternity of rolling an enormous bolder up a hill, only to watch it roll back down again. The angle of elevation of the hill is 35° and the peak of the hill is 325 feet above the ground level. Draw a diagram to illustrate this scenario and calculate the distance Sisyphus must roll the boulder. Geometry Fall 2008 Name: ________________________ Warm-up In Greek mythology, Sisyphus was condemned to an eternity of rolling an enormous bolder up a hill, only to watch it roll back down again. The angle of elevation of the hill is 35° and the peak of the hill is 325 feet above the ground level. Draw a diagram to illustrate this scenario and calculate the distance Sisyphus must roll the boulder. Geometry Fall 2008 Name: ________________________ Unit 7 Study Guide Section 8.1 Similarity in Right Triangles Solve and simplify radical expressions (square roots) Find the geometric mean between two numbers Set up geometric mean statements and proportions and solve for unknown values in right triangles Section 8.2 The Pythagorean Theorem State and prove the Pythagorean Theorem Apply the Pythagorean Theorem to right triangles in order to find missing side lengths Section 8.3 The Converse of the Pythagorean Theorem State the Converse of the Pythagorean Theorem Determine whether a triangle is right, acute, or obtuse by applying the Pythagorean Theorem, Acute Triangle Theorem, and Obtuse Triangle Theorem Determine whether or not a triangle can exist based on given side lengths Section 8.4 Special Right Triangles Calculate missing side lengths of 45°-45°-90° and 30°-60°-90° triangles Section 8.5 & 8.6 The Sine, Cosine, & Tangent Ratios Evaluate trigonometric functions using a calculator Apply SOHCAHTOA to right triangles in order to set up sin, cos, and tan ratios Use the sin, cos, and tan ratios to determine missing side lengths in triangles Evaluate inverse trigonometric functions using a calculator Use the inverse trigonometric functions to determine missing angle measures in triangles Section 8.7 Real World Applications Apply right triangle trigonometry (sin, cos, tan) to real world situations Geometry Fall 2008 Name: ________________________ Unit 7 Review Bingo Directions: Solve the following problems and choose 24 of your solutions to place in the boxes of the BINGO board in any order you choose. Section 8.1 Similarity in Right Triangles Directions: Simplify the following radical expressions (square roots). Be sure to fully simplify your answer. 5 = 5 2= 121 = 6 14 2 = 40 = 72 = 10 3 = 32 4 8 = 10 = Directions: Find the geometric mean between the given numbers. Be sure to fully simplify your answer. The geometric mean between 6 and 9 = _______ The geometric mean between 4 and 5 = _______ The geometric mean between 8 and 7 = _______ Directions: Set up geometric mean statements and proportions to solve for x, y, and z. Be sure to fully simplify your answer. Section 8.2 The Pythagorean Theorem Directions: Apply the Pythagorean Theorem to find the missing side lengths. Section 8.3 The Converse of the Pythagorean Theorem Directions: Determine whether the triangle with the given dimensions is right, acute, obtuse, or “does not exist.” 8, 14, 17 __________ 8, 8 3 , 16 __________ 4, 9, 15 __________ 5, 6, 7 __________ Section 8.4 Special Right Triangles Directions: Calculate missing side lengths of the triangles. Section 8.5 & 8.6 The Sine, Cosine, & Tangent Ratios Directions: Evaluate the following trigonometric functions using a calculator. Round answers to the nearest hundredth. sin( 52) cos( 25) tan( 70) Directions: Evaluate the following inverse trigonometric functions using a calculator. Round answers to the nearest whole number. sin 1 (0.9962) 1 cos 1 2 2 7 tan 1 5 Directions: Apply SOHCAHTOA to the right triangle in order to evaluate the sin, cos, and tan functions. Be sure to fully simplify and rationalize your answer. sin( ) cos( ) tan( ) Directions: Use the sin, cos, and tan ratios to determine the missing side lengths in the triangles. Round answers to the nearest hundredth. Directions: Use the inverse trigonometric functions to determine the missing angle measures. Round answers to the nearest whole number. Section 8.7 Real World Applications A sailboat 10 miles due north of the coast is approaching a dangerous rip tide. A harbor patrol station on the coast is aware of the rip tide and has calculated that it is 27 miles from the patrol station. If the boat comes within 30 miles of the rip tide, the patrol station must send out an emergency radio frequency to warn the boat. Fill in the above information into the diagram at right and calculate the angle θ (to the nearest whole number) and the distance d (round to the hundredths) between the sailboat and the rip tide. θ= d= Should the patrol station send out an emergency radio warning? FREE SPACE Geometry Fall 2008 Name: ________________________ Exit Ticket Proof of the Pythagorean Theorem: Given: ACB is a right angle. Prove: a 2 b 2 c 2 Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6) Geometry Fall 2008 Name: ________________________ Exit Ticket Proof of the Pythagorean Theorem: Given: ACB is a right angle. Prove: a 2 b 2 c 2 Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6)