SOLUTION: Hi there! I need some step by step help with law of sines solving two triangles Here's my question from my worksheet: Given triangle ABC with a=13, b=14 and A=35degrees find

Question 141838: Hi there! I need some step by step help with law of sines solving two triangles
Here's my question from my worksheet:
Given triangle ABC with a=13, b=14 and A=35degrees find c. Round your answer to two decimal places. The answer for that is c= 21.69 OR 1.24
I worked out the problem and got c= 21.69, I just don't know how to get 1.24!
Could you show me step by step how to get 1.24! Thanks a lot!! =]
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given triangle ABC with a=13, b=14 and A=35degrees find c.
Round your answer to two decimal places.
The answer for that is c= 21.69 OR 1.24
I worked out the problem and got c= 21.69,
I just don't know how to get 1.24!
Could you show me step by step how to get 1.24!
----------------------
Law of Sines:
SinB/14 = Sin35/13
SinB = (14/13)sin(35)=0.6176977
B = sin^-1(0.6176977)= 38.148 degrees
-----------------
Then Angle C = 180-(35+38.148) = 106.85
---------------
Solving for "c":
c/sinC = 13/sin(35)
c = (sin106.85)[13/sin(35)]
c = 21.69
----------------
How to get c = 1.24!
B = sin^-1(0.6176977) = 180-38.148 = 141.852
--------
Then Angle C = 180-(35+141.852) = 3.148 degrees
---------
solving for "c"
c/sinC = 13/sin(35)
c = sin(3.148)[13/sin(35)]
c = 1.244645...
-----------------------
So you see the inverse sine of (0.6176977) could have two values
and the resulting triangles would be different.
-----------------------
Cheers,
Stan H.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
using the law of sines __ sin(B)=(sin(A))*14/13

so B=38.15� (approx) OR B=141.85� (approx) __ sine is positive in both quadrant I and II

so does C=3.15� OR does C=106.85� __ this is the source of the dual answer
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