SOLUTION: In triangle ABC . B = 60 deg c = 7cm and a = 10cm If M is the midpoint of BC find without using tables, the lengths of AM and AC.
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Question 1203007: In triangle ABC . B = 60 deg c = 7cm and a = 10cm If M is the midpoint of BC find without using tables, the lengths of AM and AC. Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! In triangle ABC . B = 60 deg c = 7cm and a = 10cm If M is the midpoint of BC find without using tables, the lengths of AM and AC.
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b = AC
Use the Cosine Law to find b
b^2 = a^2 + c^2 - 2ac*cos(60)
b^2 = 100 + 49 - 2*10*7*0.5 = 149 - 70 = 79
b = sqrt(79)
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Use the Law of Sines to find angle A:
sin(B)/b = sin(A)/a
sin(A) = a*sin(B)/b = 10*sin(60)/sqrt(79)
sin(A) = 0.97435
A = 77 degs
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Angle A = 180 - (77+60) = 43 degs
A/2 = 21.5 degs
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Use the Cosine Law to find AM
