Question 1049970: Solve this Triangle
Angle B is 103 degrees and side a is 13.1cm and side c is 10.0cm
Thanks very much Found 3 solutions by stanbon, josgarithmetic, addingup:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Solve this Triangle
Angle B is 103 degrees and side a is 13.1cm and side c is 10.0cm
Use the Law of Cosines to get:
b^2 = a^2 + c^2 - 2ac*Cos(B)
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b^2 = 330.54
b = 18.18
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Use the Law of Sines to get:
Sin(A)/Sin(B) = a/b
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Sin(A) = (13.1/18.18)*Sin(103) = 0.7021
A = arcsin(0.7021) = 44.6 degrees
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C = 180-(103+44.6) = 32.4 degrees
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Use Law of Sines to solve for "c"::
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Cheers,
Stan H.
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The description as described here puts angle at point B accross from side b, and the angle at point B is between sides a and c. Law Of Cosines will let you solve for side b.
----using degrees.
, as an approximation.
Law Of Sines can let you find angle at A or C.
Sum of angle measures to 180 degrees will let you find angle at C or A.
You can put this solution on YOUR website! "SAS" is when we know two sides and the angle between them, which is the case in your problem we need to find side b and angles A and C:
:
b^2 = a^2+c^2−2ac*(cosB)
b^2 = 13.1^2+10.0^2-2(13.1*10.0)*(cos103) Use your calculator and you'll get:
b = 18.18
Now we use the The Law of Sines to find the smaller of the other two angles. The smaller angle is the one facing the shorter side.
sin C/c = sin B/b
sin C/10 = sin 103/18.18
sin C = sin 103*10/18.18
sin C = 0.535957
C = sin^-1 (0.535957)
C = 32.41 degrees
Now we need one more angle. The sum of the angles of ALL triangles add up to 180 degrees. And we have:
B = 103
C = 32.41
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135.41
A = 180-135.41 = 44.59
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