Assume each triangle has the given measurements. Solve for the remaining sides and angles.
a) a=5, b=8, c=9
b) a=4, b=5, A=40°
a) Use the Law of Cosines: c2 = a2 + b2 - 2·a·b·cos(C)
substitue in the values: 92 = 52 + 82 - 2·5·8·cos(C)
evaluate: 81 = 25 + 64 - 80·cos(C)
add: 81 = 89 - 80·cos(C)
subtract: -8 = -80·cos(C)
divide: 1/10 = cos(C)
cos-1(1/10) = C
C = 84.26o
You can now find either angle(B) or angle(C) by using the Law of Sines or the Law of Cosines.
Then, you can find the remaining angle by subtaction from 180o.
Hint: if you are to find all three angles, find the largest angle first by the Law of Cosines; using the Law of Sines to find the largest angle can give you an incorrect answer if the angle is greater than 90o.
b) Use the Law of Sines: sin(B) / 5 = sin(40o) / 4
cross multiply: 4·sin(B) = 5·sin(40o)
divide: sin(B) = 5·sin(40o) / 4
B = sin-1( 5·sin(40o) / 4 )
B = 53.46o
Now, find the third angle by subtaction from 180o.
Then, find the last side by the Law of Sines.