Question

How to do this step by step?

Answer 1

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+20^2-14^2)/200
cos A = (100+400-196)/200
cos A = (500-196)/200
cos A = (304)/200
cos A = (1.52)
A = cos^-1(1.52) = 40.54 degrees

cos B = (c^2+a^2-b^2)/2ca
cos B = (20^2+14^2-10^2)/280
cos B = (400+196-100)/280
cos B = (496)/280
cos B ≈ 1.77
B = cos^-1(1.77) = 27.66 degrees

we have two methods left to find the measure of angle C:
method 1 :
cos C = (a^2+b^2-c^2)/2ab
cos C = (14^2+10^2-20^2)/140
cos C = (196+100-400)/140
cos C = (-104)/140
cos C ≈ -0.74

C = cos^-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