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Do Now: • A golf ball is launched at 20 m/s at an angle of 38˚ to the horizontal. 1. What is the vertical component of the velocity? 2. What is the horizontal component of the velocity? 3. What does the word “component” mean to you? Objective- To solve problems involving the Pythagorean Theorem and Trig Identities For Right Triangles Only! leg hypotenuse - always opposite the right angle leg Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! hypotenuse leg a c b leg Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! hypotenuse ba c ba Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! Pythagorean Theorem a c b a b c 2 2 2 Solve for x. a b c 2 6 x 8 2 2 6 8 x 2 36 64 x 2 100 x 2 2 2 100 x 10 x 2 x 10 or 10 Solve for y. a b c 2 2 2 7 4 y 2 49 16 y 2 65 y 2 7 4 y 2 2 65 y 2 65 y y 65 or 65 y 8.1 Solve for t. 6 a b c 2 15 2 t 6 15 2 t 36 225 36 36 2 t 2 2 2 t 189 2 t 189 t 189 t 13.7 2 Pythagorean Triples 3 4 5 6 8 10 9 12 15 12 16 20 Pythagorean Triples 3 4 5 5 12 13 7 24 25 6 8 10 10 24 26 14 48 50 9 12 15 15 36 39 21 72 75 12 16 20 12 9 15 To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet. a b c 2 4 ft. x 10 ft. 2 2 4 10 x 2 16 100 x 2 116 x 2 2 2 116 x 2 x 116 x 10.8 A car drives 20 miles due east and then 45 miles due south. To the nearest hundredth of a mile, how far is the car from its starting point? a b c 2 20 miles x 2 20 45 x 2 400 2025 x 2 2425 x 2 45 miles 2 2 2 2425 x 2 x 2425 x 49.24 TRIGONOMETRIC IDENTITIES SohCahToa OPP SIN= HYP OPP TAN= ADJ ADJ COS= HYP OPP SIN= HYP X Soh ADJ COS= HYP X Cah OPP TAN= ADJ X Toa SAMPLE RIGHT TRIANGLE PROBLEMS 1.) x 20 A B z 30 Ø C y Find the values to the nearest tenth of: B/A A.) sin Ø = _______ A.) XY = ________ 11.5 C/A B.) cos Ø = _______ 23.1 B.) YZ = ________ B/C C.) tan Ø = _______ 60 A ship sails 340 kilometers on a bearing of 75 degrees. A. How far north of its original position is the ship? B. How far east of its original position is the ship? B A. Cos 75 = A 340 B. Sin 75 = B 340 A 340 75