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

$c = (21sin43)/sin102$

$c= 14.6$