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Title: How would I solve these law of sines and cosines problems? Post by: tyhunt04 on Jul 5, 2013 1. A=58 a=11b=12.8
2. A=74 a=13 b=25 3. B= 8.25 a=26 c=18 Title: How would I solve these law of sines and cosines problems? Post by: jtwalkee on Jul 5, 2013 This is the pattern that solves each of #1, #2
1) Compute sin(A) / a. 2) Compute sin(B) = [(b * sin(A)) / a] 3) Compute B by taking the inverse sine of sin(B) 4) Knowing the two angles A and B, subtract their sum from 180 degrees to find C. 5) Compute sin(C) - easy 6) Since: sin(C).....sin(A) --------- = --------- ...c...........a 7) a * sin(C) = c * sin(A) 8) c = ((a * sin(C)) / sin(A)) 9) Since you already know a, sin(A), and sin(C) this is nothing but arithmetic. . 1) Since (sin(58) / 11) = 0.07710, (sin(B) / 12.8) = 0.07110. So: sin(B) = (12.8) * 0.07110 = 0.98682. Take the inverse sine of this to find the angle B = 80.68720 degrees. We know that the sum of the angles of a triangle is 180 degrees, so C = 180 - (58 + 80.68720) = 180 - 138.68720 = 41.31280 degrees. Since we know that sin(C) / c = 0.07110 and that sin(C) = 0.66017. So: 0.66017 / c = 0.07110.....Multiply both sides by c (0.66017) = (0.07110) * c.....Divide both sides by 0.07110 c = (0.66017 / 0.07110) = 9.28508 Summarizing - with angles in degrees --------------------------- A = 58, B = 80.68720, C = 41.31280 a = 11, b = 12.8, c = 9.28508 --------------------------- . Now that you have the steps and an example to follow #2 is easy. I'll leave that one for you to do so that you'll learn it and not just another read another identical type of problem. :) (I'm an ex-teacher - you know how it is - I want you to learn how to do these so that when your exam comes up you will have solved one of them.) E-mail me if you get stuck. But I'm sure that you can handle this one easily. -------------- 3) This requires the law of cosines. b^2 = a^2 + c^2 - 2ac*cos(B) Since B = 8.25 degrees, cos(B) = 0.98965 So b^2 = 26^2 + 18^2 - (2 * 26 * 18 * 0.98965) = 676 + 324 - 926.31370 = 1000 - 926.31370 = 73.68630 b = sqrt(b^2) = 8.58407 Now we know sin(B) / b = (0.14349 / 8.58407) = .01672 So sin(C) / c = sin(A) / a = 0.01672 So (sin(C) / 18) = 0.01672......Multiply both sides by 18, getting: sin(C) = 0.30089 and taking the inverse sine, C = 17.51111 degrees Since A + B + C = 180 degrees, A = (180 - 8.25 - 17.51111) = A = 154.23889 degrees Summarizing - with all angles in degrees ------------------------ A = 154.23889, B = 8.25, C = 17.5111 a = 26, b = 8.58407, c = 18 ------------------------ . |