
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 13th, 2017, 06:37 AM  #1 
Newbie Joined: May 2017 From: your ass Posts: 2 Thanks: 0 
So I'm studying math for tomorrow's exam and got onto this problem. The book states that you can use the law of Sines (sinA/a = SinB/b = SinC/c) in the (AAS, ASA, SSA) conditions to solve the triangle, and use the law of Cosines ( a^2 = b^2 + c^2  2bc cosA , ...etc.) to solve triangles in the (SSS, SAS) conditions. Now I have this Triangle △ABC: ∠A,C = unknown, ∠B = 36°, b = unknown, c = 5, a = 7. The triangle here is from the SAS condition so we have to use the law of Cosines to find the unknown values. To find the missing side (b): b^2 = a^2 + c^2 2ac cosB b^2 = 7^2 + 5^2 2(7)(5)cos36° b ≈ 4.2 and here is where the problem starts, since we have now 3 known sides and 1 known angle, we can use both the law of Sines and the law of Cosines to find the remaining Angles, however, when I use the law of Sines I get a different answer from when I use the law of Cosines. Here, let's try to find ∠A using the law of Cosines: a^2 = b^2 + c^2  2bc cosA 7^2 = 4.2^2 + 5^2  2(4.3)(5)cosA 7^2 4.2^2  5^2 = 2(4.3)(5)cosA cosA = (7^2  4.2^2  5^2)/[2(4.3)(5)] cosA = 0.1514 ∠A = inverse cos(0.1514) ∠A ≈ 99° and now let's try to find it using the law of Sines: SinA / a = SinB / b SinA / 7 = Sin36 / 4.2 SinA = 7 Sin36 / 4.2 SinA = 0.97964 ∠A = inverse sin0.97964 ∠A ≈ 78° The answers were different using each law  where's the fault? Is it my calculations? Is it the law was incorrect? Need quick help please. Last edited by skipjack; May 13th, 2017 at 08:19 AM. 
May 13th, 2017, 09:09 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,172 Thanks: 1285 
If you use 4.167 instead of 4.2, you get 80.9°. As the angle is obtuse, you need to subtract this from 180° to get 99.1°, which is about the same as your earlier value. It isn't immediately obvious that the angle at A is obtuse, but you could calculate the angle at C instead, etc. 
May 13th, 2017, 01:10 PM  #3 
Newbie Joined: May 2017 From: your ass Posts: 2 Thanks: 0 
how did you know that it was obtuse? when i calculate the C the answer was 44.8 using both laws, and i was able to find A by subtracting B and C from 180 (180  36  44.8 = 100) which is around 99.1 but i didn't get how you found that A is obtuse and went for the 99.1 over the 80.9 

Tags 
cosines, law, sines 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
OneSided Limits with Sines and Cosines  njuice8  Calculus  1  May 19th, 2013 09:01 PM 
Law of sines/cosines  jkh1919  Algebra  1  November 26th, 2011 02:27 PM 
Law of Cosines PWW  molokach  Algebra  0  March 18th, 2011 09:30 AM 
Equivalence of the Law of Sines, PT, and Law of Cosines  molokach  Algebra  19  February 25th, 2011 05:02 PM 
Help: simplify this expression with just sines and cosines?  Stephanie7  Algebra  1  April 19th, 2009 01:04 PM 