In the triangle shown below, what are the measures of angles a, b, and c? round

The answer to your question is

A = 29.6°

B = 115.4°

C = 35°

Step-by-step explanation:

Process

1.- Use the Cosines law to answer this question

     c² = a² + b² - 2abcosФ

Solve for cos Ф

    cos Ф = (c² - a² - b² )/ -2ab

Substitution

    cosФ = (7² - 6² - 11²) / (-2)(6)(11)

    cosФ = (49 - 36 - 121) / -132

    cos Ф = -108 / -132

    cos Ф = 0.818

           Ф = 35° = C

Find B

   cos Ф = (b² - a² - c²)  / (-2ac)

   cos Ф = (11² - 6² - 7²)  / (-2)(6)(7)

   cos Ф = ( 121 - 36 - 49) / -84

  cos Ф = 36 / -84

  cos Ф = -0.429

         Ф = 115.4° = B

2.- Find a

The sum of the internal angles in a triangle equals 180°

     A + B + C = 180  

    A + 115.4 + 35 = 180

    A = 180 - 115.4 - 35

    A = 29.6°  

There's a rule where the the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side So, add the two smallest numbers of each triangle and see if it is greater than the biggest number:

A: 5 + 12 = 17, and the longest side is 17. 17 isn't more than 17, so the answer isn't A.

B: 10 + 15 = 25, and the longest side is 24. 25 is more than 24, so 'B' can be a triangle! We know this is an answer, but we should always check to see if any other answers work.

C: 9 + 11 = 20, and the longest side is 22. 20 isn't more than 22, so the answer isn't 'C'

D: 7 + 6 = 13, and the longest side is 21. 13 isn't more than 21, so the answer isn't 'D'

Answer 'B' is the only one that can  make a triangle, so it's the right answer!

Hope I helped, let me know if you have any questions :)