Just curious, but why doesnt this work? law of sin states: sin(A) sin(B) sin(C) -------- = -------- = -------- a b c law of cosines: a^2 = b^2 + c^2 - 2bc sin A b^2 = a^2 + c^2 - 2ac sin B c^2 = a^2 + b^2 - 2ab sin C given the sides: a = 13/3 b = 8.5 c = 6.8 use the law of cos to find angle A. cos(A) = a^2 - b^2 - c^2 --------------- -2bc you get: sin(A) = 0.8625624 A = 30.39 now, we use the law of sines to find angle B: sin(A) sin(B) -------- = -------- a b 0.5059506 sin(B) ----------- = -------- 13/3 8.5 sin(B) = 0.992441748 B = 82.95 the problem is that if we use the law of cosines, we get a different value...: cos(B) = b^2 - a^2 - c^2 --------------- -2ac you get B = 97.05 how come when using the different equations, you get different answers? I found that the answer using law of cos both times is correct where the other is not. This was just bugging the heck out of me because I can not figure out what Im doing wrong. I know for a fact these law of sins and coss have been prooven many times are not flawless. Thanx for your help!!! Dwiel ~ Tazzel3d

I believe the law of cosine must somehow involve cosine in the equation somewhere.

The correct equation is: c^2 = a^2 + b^2 - 2ab*cos(feta)

Your side lengths are funky.

 (13/3)² - (8.5²) - (6.8²)     -99.71222222--------------------------- = -------------- = -1.725124952       -(8.5 * 6.8)                -57.8 

...which clearly exceeds the bounds for sine and cosine (1).

[Edit: Formatting.]

[edited by - Oluseyi on May 10, 2002 1:42:54 PM]

I didn''t look through the whole thing in detail, but the two angles you come up with are complements in that they add up to pi. I suspect one is negative and is the result of the differant ranges on acos and asin. asin returns values in the range from -pi/2 to pi/2 while acos returns values in the range of 0 to pi. So if the angle is in the second quadrant asin is going to give you the angle - pi and say it is in the fourth quadrant. Well, you used degrees, but pi is 180 degrees.

Oluseyi: You forgot to divide by 2

Again, Tazzel3D''s equations for cosine laws are incorrect. Clearly, a cosine is needed in the equation. Tazzel3D is using sine in a cosine equation...

Your equations are incorrect as DigiCube pointed out. The correct one is

c² = a² + b² - 2ab*cos(C) where C is the angle opposed to side c

Cédric

You guys all have the Law of Cosines correct, but when you solve for the cosine of an angle, you keep doing it wrong.

c^2 = a^2 + b^2 - 2ab cos(C)cos(C) = (a^2 + b^2 - c^2) / (2ab) 

You had

cos(C) = (a^2 - b^2 - c^2) / (2ab) 

Thus, using the side length of 13/3, 8.5, and 6.8, you get:

cos(A) = (8.5^2 + 6.8^2 - (13/3)^2) / (2 * 8.5 * 6.8) = 0.8626A = 30.39 degreescos(B) = ((13/3)^2 + 6.8^2 - 8.5^2) / (2 * (13/3) * 6.8) = -0.1227B = 97.05 degreescos(C) = ((13/3)^2 + 8.5^2 - 6.8^2) / (2 * (13/3) * 8.5) = 0.6080C = 52.56 degreessin(A) = 0.5059sin(B) = 0.9924sin(C) = 0.7940A / sin(A) = 8.566B / sin(B) = 8.565C / sin(C) = 8.564 

Thus, the Law of Sines holds true. Note that the slight differences were due to intermediate rounding errors.

[edited by - Aprosenf on May 10, 2002 6:23:12 PM]