Question 445790: In a triangle, two sides that measure 8cm and 12cm form a angle that measures 80 degrees. Find, to the nearest degree, the measure of the smallest angle in the triangle.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! In a triangle, two sides that measure 8cm and 12cm form a angle that measures 80 degrees. Find, to the nearest degree, the measure of the smallest angle in the triangle.
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Given triangle with angles ABC and corresponding opposite sides abc.
C=80º, a=12, b=8
Use Law of Cosines to find the third side, then use Law of Sines to find the smallest angle.
Law of Cosines: c^2=a^2+b^2-2ab cos C
c^2=8^2+12^2-2(8*12)cos 80
c^2=64+144-(192*cos 80)
c^2=208-33.34=174.66
c=13.22
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Using Law of Sines:
sin C/side c=sin B/side b
sin 80/13.22=sin B/8
sin B=8 sin 80/13.22=.59595
B=37º
A=180-37-80=63º
Therefore, B is the smallest angle in the triangle at 37º
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