Question 1042353
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Solve the triangle ABC. (using the law of cosines)

a=10,b=12,c=16
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This assignment is to find the angles of the given triangle.

Use the Law of Cosines.

{{{c^2}}} = {{{a^2 + b^2 - 2ab*cos(C)}}},   or

{{{16^2}}} = {{{10^2 + 12^2 - 2*10*12*cos(C)}}},   or

256 = 100 + 144 - 240*cos(C),   or

256 - 100 - 144 = - 240*cos(C),   or

12 = -240*cos(C),   or

cos(C) = {{{-12/240}}} = {{{-1/20}}}.   --->  angle C = {{{arccos(-1/20) + pi}}} = {{{pi - arccos(1/20)}}}   (an obtuse angle).

Doing by the same way, find cos(B) and cos(C).

This is the way.
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