Question

anonymous 4 years ago The sides of a triangle measure 14.9 centimeters, 23.8 centimeters, and 36.9 centimeters. Find the measure of the angle with the least measure.

Answer 1

Using the Law of Cosines
cos (A) = b^2 + c^2 -a^2 / 2bc

cos (A) = (23.8*23.8 + 36.9*36.9 - 14.9*14.9) / (2*23.8*36.9)
cos (A) = 0.9713055954
Angle = 13.759 Degrees

cos (A) = (36.9*36.9 + 14.9*14.9  -23.8*23.8 ) / (2*36.9*23.8)
cos (A) = 0.9250286463
Angle = 22.327 Degrees

cos (A) = (14.9*14.9  + 23.8*23.8 -36.9*36.9) / (2*14.9*23.8)
cos (A) = -0.808132649
Angle = 143.91 Degrees

So, the smallest angle is 13.759 Degrees