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mathnstuff.com/math/precalc/MAT129fa25/p.22.htm © 2025 A2, Agnes Azzolino Law of Sines; Law of Cosines, Text 10.1, 10.2, PG. 762, 776 |
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10.1 - Non-right Triangles: Law of Sines, pg. 762, Learning Objectives * Use the Law of Sines to solve oblique triangles. * Find the area of an oblique triangle using the sine function. * Solve applied problems using the Law of Sines. |
Law of Sines sin (A) / a = sin(B) / b = sin(C) / c a / sin (A) = b / sin (B) = c / sin (C) |
Law of Sines a = (c*sin(A) / sin(C) a = (b*sin(A) / sin (B) b = (a*sin(B)) / sin (A) b = (c*sin(B)) / sin (C), etc. |
10.2 - Non-right Triangles: Law of Cosines, pg. 776, Learning Objectives * Use the Law of Cosines to solve oblique triangles. * Solve applied problems using the Law of Cosines. * Use Heron’s formula to find the area of a triangle. |
Law of Cosines
a2 = b2 + c2 - 2bccos(A) b2 = a2 + c2 - 2accos (B) c2 = a2 + b2 - 2abcos(C) |
cos(A) = ( b2 + c2 - a2) / ( 2(b)(c) )
cos(B) = ( a2 + c2 - c2) / ( 2(a)(c) ) cos(C) = ( a2 + b2 - c2) / ( 2(a)(b) ) A = cos-1 [ b2 + c2 - a2) / (2(b)(c) ) ] B = cos-1 [ a2 + c2 - b2) / (2(a)(c) ) ] C = cos-1 [ a2 + b2 - c2) / (2(a)(b) ) ] |