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Myrecia Davis Amaana Hinds 6th Study Guide Law of Sine The Law of Sine provides a formula that relates the sides with the angles of a triangle. This formula allows you to easily find the side length or the angle. The law of sin has angles and its opposite sides. The law of sins can have two sides, one degree, and two degrees. Formula Examples 1. Since this problem uses sides a and b, we need to know the sides of b. Myrecia Davis Amaana Hinds 2. Since this problem uses side r and t, we need to know <S. 6th Myrecia Davis Amaana Hinds Practice Problems: For addition explaining, you can refer to the (pgs.582-585) in your textbook. 1. 2. Video https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sinescosines/v/law-of-s 6th Myrecia Davis Amaana Hinds Law of Sine Practice Problem Solutions 1. 2. First find m<A by using the Triangle Theorem. Now, use the law of sine to help set up ratios. 6th Myrecia Davis Amaana Hinds The Law of Cosine Definition: The Square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them. The law of cosines has two sides, or three sides. Formula Examples 1. In, m<C = 42º, a = 19 and b = 26. Find the length of side c, to the nearest integer. 6th Myrecia Davis Amaana Hinds 6th 2. This problem involves all three sides but only one angle of the triangle. This fits the profile for the Law of cosines. Myrecia Davis Amaana Hinds Practice Problems If you need more explaining, you can refer to the (pgs.591-598). . 2. Video https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sinescosines/v/law-of-cosines-example 6th Myrecia Davis Amaana Hinds Law of Cosine Practice Problem Solutions 1. Sin3522 = SinB38 Sin B = 38 x Sin3522 = 0.9907 2. Apply the law of cosines that involves θ. => b2 = a2 + c2 - 2ac cosθ => b2 = 102 + 52 - 2 * 10 * 5 cos45o => b2 = 100 + 25 - 100 * = 125 - 70.9 = 54.1 => b = 7.4 (approx) 12√ 6th