a = b 2 + c 2 − 2 b ∗ c ∗ c o s ∠ A a = \sqrt{b^2 +c^2 -2b*c*cos\angle{A}} a = b 2 + c 2 − 2 b ∗ c ∗ cos ∠ A
a = 72 6 2 + 93 8 2 − 2 ∗ 726 ∗ 938 ∗ c o s 78 ° 4 8 ′ = 1650.168 a = \sqrt{726^2 +938^2 -2*726*938*cos78\degree 48'} = 1650.168 a = 72 6 2 + 93 8 2 − 2 ∗ 726 ∗ 938 ∗ cos 78°4 8 ′ = 1650.168
a / s i n ∠ A = b / s i n ∠ B a / sin\angle A = b/sin\angle B a / s in ∠ A = b / s in ∠ B
s i n ∠ B = b ∗ s i n ∠ A / a = 726 ∗ s i n 78.8 ° / 1650.168 = 0.432 sin\angle B = b*sin\angle A / a = 726*sin78.8\degree / 1650.168 = 0.432 s in ∠ B = b ∗ s in ∠ A / a = 726 ∗ s in 78.8°/1650.168 = 0.432
if ∠ B > 90 ° , \angle B > 90\degree, ∠ B > 90° , when ∠ C < 11 ° 1 2 ′ \angle C < 11\degree 12' ∠ C < 11°1 2 ′ and side the smallest, but the smallest side is b,
therefore ∠ B < 90 ° , \angle B < 90\degree, ∠ B < 90° ,
∠ B = 28.59 ° = 28 ° 3 6 ′ \angle B = 28.59\degree = 28\degree36' ∠ B = 28.59° = 28°3 6 ′
∠ C = 180 ° − ∠ A − ∠ C = 180 ° − 28 ° 3 6 ′ − 78 ° 4 8 ′ \angle C = 180\degree -\angle A -\angle C = 180\degree - 28\degree36' - 78\degree 48' ∠ C = 180° − ∠ A − ∠ C = 180° − 28°3 6 ′ − 78°4 8 ′
∠ C = 72 ° 3 6 ′ \angle C = 72\degree36' ∠ C = 72°3 6 ′
answer :
a = 1650.168 ∠ C = 72 ° 3 6 ′ ∠ B = 28 ° 3 6 ′ a =1650.168\\\angle C = 72\degree36'\\\angle B = 28\degree36' a = 1650.168 ∠ C = 72°3 6 ′ ∠ B = 28°3 6 ′
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