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7.6 Law of Sines • Use the Law of Sines to solve triangles and problems In trigonometry, we can use the Law of Sines to find missing parts of triangles that are not right triangles. A Law of Sines: In ABC, c b sin A = sin B = sin C a b c C a B Find p. Round to the nearest tenth. Law of Sines Cross products Divide each side by sin Use a calculator. Answer: to the nearest degree in , Law of Sines Cross products Divide each side by 7. Solve for L. Use a calculator. Answer: a. Find c. Answer: b. Find mT to the nearest degree in RST if r = 12, t = 7, and mR = 76. Answer: The Law of Sines can be used to “solve a triangle,” which means to find the measures of all of the angles and all of the sides of a triangle. . Round angle measures to the nearest degree and side measures to the nearest tenth. We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find Angle Sum Theorem Add. Subtract 120 from each side. Since we know and f, use proportions involving To find d: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator. To find e: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator. Answer: Round angle measures to the nearest degree and side measures to the nearest tenth. We know the measure of two sides and an angle opposite one of the sides. Law of Sines Cross products Divide each side by 16. Solve for L. Use a calculator. Angle Sum Theorem Substitute. Add. Subtract 116 from each side. Law of Sines Cross products Divide each side by sin Use a calculator. Answer: a. Solve Round angle measures to the nearest degree and side measures to the nearest tenth. Answer: b. Round angle measures to the nearest degree and side measures to the nearest tenth. Answer: A 46-foot telephone pole tilted at an angle of from the vertical casts a shadow on the ground. Find the length of the shadow to the nearest foot when the angle of elevation to the sun is Draw a diagram Draw Then find the Since you know the measures of two angles of the triangle, and the length of a side opposite one of the angles you can use the Law of Sines to find the length of the shadow. Law of Sines Cross products Divide each side by sin Use a calculator. Answer: The length of the shadow is about 75.9 feet. A 5-foot fishing pole is anchored to the edge of a dock. If the distance from the foot of the pole to the point where the fishing line meets the water is 45 feet, about how much fishing line that is cast out is above the surface of the water? Answer: About 42 feet of the fishing line that is cast out is above the surface of the water. Pre-AP Geometry: Pg. 381 #15, 16 – 32 evens, 42 Geometry: Pg. 381 #15, 16 – 28 evens