Law of cosines: a2 = b2 + c2 - 2bccos (A) Find the measure of Q, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. Round the measure to the nearest whole degree.

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°.