Expert: Ahmed Salami - 9/2/2009

Question
having trouble understanding the steps to solve each triangle.  here is a couple of my problems if you can help.  B = 42 deg., C = 68 deg., a = 10.  next problem A = 40 deg., B = 14 deg., a = 52.  maybe with the answers to these i can apply to my other problems.  my math teacher is not very helpful even though i went to her and asked for more help that i did not understand the homework.  hope u can help thanks mikie

Answer
Hi Mikie,
You need to always remember that the sum of the angles in a triangle equals 180 degrees.
1) B = 42°, C = 68°, a = 10
But we know that A + B + C = 180°
So, A = 180 - (B + C)
     = 180 - (42 + 68) = 180 - 110 = 70°
From the law of sines,
a/sinA = b/sinB = c/sinC
Therefore,
10/sin70 = b/sin42
10/0.9397 = b/0.6691
b = 10(0.6691)/0.9397
 = 7.12
and
10/sin70 = c/sin68
10/0.9397 = c/0.9272
c = 10(0.9272)/0.9397
 = 9.87

2)A = 40°, B = 14°, a = 52
A + B + C = 180°
C = 180 - (A + B)
 = 180 - (40 + 14) = 180 - 54 = 126°
From the law of sines,
a/sinA = b/sinB = c/sinC
Therefore,
52/sin40 = b/sin14
52/0.6428 = b/0.2419
b = 52(0.2419)/0.6428
 = 19.57
and
52/sin40 = c/sin126
52/0.6428 = c/0.8090
b = 52(0.8090)/0.6428
 = 65.45
Tip: Note that if you're using tables and not a calculator, sin(126) is the same as sin(180-126) i.e sin(54)

Happy to help.

Regards