The answer is 27.6
angle version of the law of cosines:
cos(C) = (a^2 + b^2 − c^2)/2ab
cos(A) = (b^2 + c^2 − a^2)/2bc
cos(B) = (c^2 + a^2 − b^2)/2ca
cos A = (b^2 + c^2 − a^2) / 2bc
cos A = (10^2+20^2-14<span>^2)/200
cos A = (100+400-196)/200
cos A = (500-196)/200
cos A = (304)/200
cos A = (1.52)
A = cos</span><span>^-1(1.52) = 40.54 degrees
cos B = (c</span>^2+a^2-b<span>^2)/2ca
cos B = (20</span>^2+14^2-10<span>^2)/280
cos B = (400+196-100)/280
cos B = (496)/280
cos B </span>≈ 1.77
B = cos<span>^-1(1.77) = 27.66 degrees
we have two methods left to find the measure of angle C:
method 1 :
cos C = (a</span>^2+b^2-c<span>^2)/2ab
cos C = (14</span>^2+10^2-20<span>^2)/140
cos C = (196+100-400)/140
cos C = (-104)/140
cos C </span>≈ -0.74
C = cos<span>^-1(-0.74) = 111.8 degrees
method 2: 40.54+27.66 = 68.2
180-68.2=111.8
The measure of angle A: 40.54
The measure of angle B: 27.66
The measure of angle C: 111.8
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