Name ________________________________________ Date __________________ Class __________________ Reteach Law of Sines and Law of Cosines You can use a calculator to find trigonometric ratios for obtuse angles. sin 115 0.906307787 cos 270 0 tan 96 9.514364454 The Law of Sines For any ABC with side lengths a, b, and c that are opposite angles A, B, and C, respectively, sin A sin B sin C . a b c Find m P. Round to the nearest degree. sin P MN sin N PM Law of Sines sin P 10 in. sin36 7 in. MN sin36 7 in. 10, m N 36 , PM 7 Multiply both sides by 10 in. sin P 10 in. sin P 0.84 m P 1 sin (0.84) Use the inverse sine function to find m P. m P 57 Simplify. Simplify. Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. 1. cos 104 ________________________ 2. tan 225 3. sin 100 _________________________ ________________________ Find each measure. Round the length to the nearest tenth and the angle measure to the nearest degree. 4. TU _________________________________________ 5. m E ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name ________________________________________ Date __________________ Class __________________ Reteach Law of Sines and Law of Cosines continued The Law of Cosines For any ABC with side lengths a, b, and c that are opposite angles A, B, and C, respectively, a2 b2 c 2 b2 a2 c 2 c 2 a2 b2 2bc cos A, 2ac cos B, 2ab cos C. Find HK. Round to the nearest tenth. HK 2 HK 2 HK HJ 2 JK 2 289 196 179.0331 ft 2(HJ)(JK) cos J Law of Cosines 2(17)(14) cos 50 Substitute the known values. 2 13.4 ft Simplify. Find the square root of both sides. You can use the Law of Sines and the Law of Cosines to solve triangles according to the information you have. Use the Law of Sines if you know • two angle measures and any side length, or • two side lengths and a nonincluded angle measure Use the Law of Cosines if you know • two side lengths and the included angle measure, or • three side lengths Find each measure. Round lengths to the nearest tenth and angle measures to the nearest degree. 6. EF _________________________________________ 8. m R _________________________________________ 7. m X ________________________________________ 9. AB ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name ________________________________________ Date __________________ Class __________________ Reading Strategies 4. 1. Law of Cosines 2. Law of Sines 3. Law of Cosines 4. 8 ft 5. 55 VECTORS 5. 2 2 ; ;1 2 2 6. 2 ; 2 2 ; 1 2 7. Possible answer: The sine of an angle is equal to the cosine of the angle’s complement: sin A cos (90 A). Reteach 1. Practice A 1. vector 2. direction 3. length 4. parallel 5. equal 6. 3, 4 7. 9, 5 8. 5, 4 9. 5 0.24 2. 1 3. 0.98 4. 24.7 m 5. 37 6. 7.0 cm 7. 58 8. 45 9. 8.1 km Challenge 1. ABC, DAE, FCE, BDF 2. 28 10. 7.3 3. 40 4. 112 sin 28 20.5m 5. sin 40 h 6. 28.1 m 7. 11. 45° 8. tan 62 28.1m x 9. 14.9 m Problem Solving 12. 14° 1. 23.3 mi 2. 32.9 ft 3. 122° 4. 60° 5. C 6. G 7. B 8. H Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry

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