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12.1 Trigonometric Ratios Trigonometry – The study of the relationship between sides and angles of triangles. B c a A C b Refer to (right) ΔABC above: Looking at A: ________ is the opposite leg Looking at B: ________ is the opposite leg ________ is the adjacent leg ________ is the adjacent leg ________ is the hypotenuse ________ is the hypotenuse Trigonometric Ratios length of leg opposite ∠A a sine of ∠A= or sin A= length of the hypotenuse c cosine of ∠A= length of leg adjacent ∠A b or cos A= length of the hypotenuse c tangent of ∠A= length of leg opposite ∠A a or tan A= length of leg adjacent ∠A b Remember: Chief Soh Cah Toa Geometry Lesson 12.1: Trigonometric Ratios Page 1 Example 1: Find the sine, cosine, and tangent of each angle. a) sin A = _____ cos A = _____ tan A = ____ B 5 3 sin B = ____ cos B = ____ tan B = _____ A C b) sin D = _____ sin E = ____ cos D = _____ tan D = ____ cos E = ____ tan E = _____ 4 E 17 15 D T F 8 5 12 c) sin R = _____ cos R = _____ tan R = ____ S sin S = ____ cos S = ____ tan S = _____ 13 R Example 2: Use a calculator to find each trigonometric ratio accurate to four decimal places. a) sin 31 = __________ b) sin 20 = __________ c) sin 70 = __________ d) cos 31 = __________ e) cos 20 = __________ f) cos 70 = __________ g) tan 31 = __________ h) tan 20 = __________ i) tan 70 = __________ Geometry Lesson 12.1: Trigonometric Ratios Page 2 Example 3: Find the missing measures in the following right triangles. a) b) 11 cm 15 cm y 42 38 x c) d) 9 cm 23 w 49 z 12 cm Example 4: At a distance of 36 meters from a tree, the angle from the ground to the top of the tree is 31. Find the height of the tree. Geometry Lesson 12.1: Trigonometric Ratios Page 3 Example 5: Find the length of the hypotenuse of a right triangle if an acute angle measures 20 and the side opposite the angle measures 410 feet. Example 6: A right triangle has legs of length 8 inches and 15 inches. Find the length of the hypotenuse and the measures of the two acute angles. Example 7: A right triangle has a leg of length 32 inches and hypotenuse of length 74 inches. Find the length of the other leg and the measures of the two acute angles. Homework: pp. 624 – 625 => 1 – 20 Geometry Lesson 12.1: Trigonometric Ratios Page 4