How do you solve the triangle given ∠B = 102°, ∠C = 43°, b = 21?

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Answer 1 · 2016-11-08T10:26:20

#hatA = 35°, a = 12.3, c = 14.6#

If you have 2 angles of a triangle, the third one can be found by subtracting the given angles from #180°#

#hatA = 180°-102°-43° =35°#

Both b and hatB are known, therefore you can use the Sine rule to find the lengths of the 2 unknown sides.

#a/sinA = b/sinB#

#a/sin35 = 21/sin102" "larr# find a

#a = (21sin35)/sin102#

#a = 12.3#

#c/sinC = b/sinB#

#c/sin43 = 21/sin102" "larr# find c

#c = (21sin43)/sin102#

#c= 14.6#