Asked by Jon
Should the triangle be solved beginning with Law of Sines of Law of Cosines. Then solve the triangle. Round to the nearest tenth. a=16, b=13, c=10.
Cosines
A=93 degrees, B=54 degrees, C=33 degrees
Cosines
A=93 degrees, B=54 degrees, C=33 degrees
Answers
Answered by
Reiny
no, two of the angles are wrong.
I found this by doing a simple check
sin93/16 , sin54/13 and sin33/10 should be the same within about 2 decimal places even allowing for your roundoff.
They are not!
A good rule to follow when all 3 sides are known, is to find the largest angle by the Cosine Law.
Your calculator has been programmed to give you the correct second quadrant angle if the cosine is negative.
so 16^2 = 13^2 + 10^2 - 2(10)(13)cosA
cosA = (169+100-256)/260 = .05
A = 87.13
Now you can safely use the Sine Law to find one of the other angles, say B
sinB/13 = sin87.13/16
sinB = .81148
B = 54.2 and using the 180ยบ sum property
C = 38.6
Only at this stage would I round off my answers.
I found this by doing a simple check
sin93/16 , sin54/13 and sin33/10 should be the same within about 2 decimal places even allowing for your roundoff.
They are not!
A good rule to follow when all 3 sides are known, is to find the largest angle by the Cosine Law.
Your calculator has been programmed to give you the correct second quadrant angle if the cosine is negative.
so 16^2 = 13^2 + 10^2 - 2(10)(13)cosA
cosA = (169+100-256)/260 = .05
A = 87.13
Now you can safely use the Sine Law to find one of the other angles, say B
sinB/13 = sin87.13/16
sinB = .81148
B = 54.2 and using the 180ยบ sum property
C = 38.6
Only at this stage would I round off my answers.
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