45 a33 b7 c37 Find LA LB LC An unsimplified exact answer for

45 a-33, b=7, c=37. Find LA, LB, LC An unsimplified exact answer for an angle might be of the form A = cos-1 [(202 + 52-122)2(20)(5)] or B = 180-(70 + 85) Exact answers may use the cosine law or be calculated as B is. Exact = Decimal (5 sym+ unit. chk-17) LA= Exact C Decimal (3 sym+unit, chk-3) C- Decimal for LB (4 sym + unit, chk-16)

Solution

4)

a = 33

b = 7

c = 37

Now law of cosines;

cos A = ( b² + c² - a² ) / 2bc = (7^2 + 37^2 – 33^2)/(2*7*37) = 329/518

A = arccos(329/518) = 50.6 degree

And

cos B = ( c² + a² - b² ) / 2ca = (37^2 + 33^2 – 7^2)/(2*33*37) = 2409/2442

B = 9.4 degree

Then C = 180 – A – B = 180 – 50.6 – 9.4 = 120 degree