Law of Sines and Cosines

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Presentation transcript:

Law of Sines and Cosines

Law of Sines The Law of Sines can be used to find side lengths and angle measures for any triangle. If △ABC has side lengths a, b, and c that are opposite angles A, B, and C, then

Law of Sines Law of Sines can be used to solve a triangle if you know the measures of two angles and any side (AAS or ASA).

Examples Find x. Round to the nearest tenth.

Examples Find x. Round to the nearest tenth.

Examples Find x. Round to the nearest tenth.

Examples Find x. Round to the nearest tenth.

Law of Cosines If △ABC has side lengths a, b, and c that are opposite angles A, B, and C, then

Law of Cosines You can use the Law of Cosines to solve a triangle if you know the measure of two sides and the included angle (SAS) or the measure of all three sides.

Examples Find x. Round to the nearest tenth.

Examples Find x. Round to the nearest tenth. x2 = 152 + 192 – (2*15*19*cos 125) x2 = 225 + 361 – (570*-.5736) x2 = 586 + 326.952 x2 = 912.952 x = 30.2

Examples Find x. Round to the nearest degree.

Examples Find x. Round to the nearest degree. 32 = 4.52 + 6.12 – 2*4.5*6.1* cos x 9 = 20.25 + 37.21 – 54.9 cos x -48.46 = -54.9 cos x .8827 = cos x cos-1 .8827 = x = 28

Solving Triangles When solving right triangles, you can use sine, cosine, or tangent. When solving other triangles, you can use the Law of Sines or the Law of Cosines, depending on what information is given.