I renamed angles D, E, F as A, B and C Also I have labeled the sides as a b c. Look at the graphic I have attached. cos (A) = (b^2 + c^2 -a^2) / 2bc cos (A) = (6*6 + 8*8 -12*12) / (2 * 6 * 8) cos (A) = (36 + 64 -144) / (96 (cos (A) = -44 / 96cos (A) =
-0.4583333333 Then we look up the arc cosine of
-0.4583333333 which equals 117.28 Degrees We now have Angle A
From here, we can use the Law of Sines: side a / sine (A) = side b / sine (B) 12 / sine (117.28) = 6 / sine (B) 12 / 0.88878 = 6 / sine (B)
sine (B) = 6 * .88878 / 12 sine (B) =
0.44439
We look up the arc sine of .44439 and it is 26.384 Degrees Angle B = 26.384 Degrees
And Angle C is easily solved. ALL triangles have angles that sum to 180 degrees. 180 = 117.28 + 26.384 + Angle C Angle C = 180 -117.28 - 26.384 Angle C = 36.336 Degrees
