We are tasked to solve for the smallest angle using the law of cosines given that the three sides of the triangle are 4,5 and 6.
a=4 , b=5, c=6
Angle 1:
cosA = 5² + 6² - 4² / 2*5*6
A=41.41°
Angle 2:
cos B = 4²+6² -5² /2*4*6
B= 55.77°
Angle C:
C = 180° - 41.41° - 55.77°
C = 82.82°
The smallest angle is A which is equal to 41.41°.
