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Geometry A Unit 9 Day 6 Notes The Law of Sines Objective: To use the law of sines to find the sides and angles of triangles (round all answers to the nearest tenth unless otherwise noted) When to use… SOH CAH TOA ______________________________________________________ sin length of side opposite length of hypotenuse cos length of side adjacent length of hypotenuse tan length of side opposite length of side adjacent Adjacent Law of Cosines________________________________________________________ In any triangle, A c b B a a 2 b 2 c 2 2bc cos A b 2 a 2 c 2 2ac cos B c 2 a 2 b 2 2ab cos C C Law of Sines__________________________________________________________ In any triangle, A c sin A sin B sin C a b c b B C a We can summarize the times that we use the Law of Sines “you know a matching set of side and angle” in a non-right triangle. AAS – given two angles and a side. In ABC , B 64, a 15, A 38. Solve for side b. ASA – given two angles and an included side. ABC , a 8, B 64, C 38. Solve the triangle. Examples: 1. How long is the base of an isosceles triangle if each leg is 27 cm and each base angle measures 23 degrees? 2. Two angles of a triangle measure 32 degrees and 53 degrees. The longest side is 55 cm. Find the length of the shortest side. 3. A fire is sighted from two ranger stations that are 5000 m apart. The angles of observation to the fire measure 52 degrees from one station and 41 degrees from the other station. Find the distance along the line of sight to the fire from the closer of the two stations. 52o 41o 4. Two markers are located at points A and B on opposite sides of a lake. To find the distance between the markers, a surveyor laid off a base line, AC , 25 m long and found that BAC 85 and BCA 66. Find AB. A C B 5. The captain of a freighter 6 km from the nearer of two unloading docks on the shore finds that the angle between the lines of sight to the two docks is 35 degrees. If the docks are 10 km apart, how far is the tanker from the farther dock? HW: Handout