A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?

  41°, 56°, 83°

Step-by-step explanation:

We can find the largest angle from the law of cosines:

  c² = a² +b² -2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°

Then the second-largest angle can be found the same way:

  B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°

Of course the third angle is the difference between the sum of these and 180°:

  A = 180° -82.8192° -55.7711° = 41.4096°

Rounded to the nearest degree, ...

  the angles of the triangle are 41°, 56°, 83°.

step-by-step explanation: