There are two non congruent triangles where B=55 degrees a=15 and b=13. Find the measures of the angles of the triangle with the greater perimeter. Round to the nearest tenth if necessary.

The side c needs to be 12.85 for the triangle to have greatest perimeter

Step-by-step explanation:

We are given;

b = 13

a = 15

Angle at b: B = 55°

Let's find side c.

Using the law of cosines, we have;

b² = a² + c² - 2ac•cos (B)

13² = 15² + c² - 2•15•c•cos (55)

169 = 225 + c² - 30c•cos (55)

c² - 30c•cos (55) + 225 - 169 = 0

c² - 30c•cos (55) + 56 = 0

c² - 30c• (0.5736) + 56 = 0

c² - 30c• (0.5736) + 56 = 0

c² - 17.208c + 56 = 0

Using quadratic formula;

c = [ - (-17.208) ± √ ((-17.208) ² - (4•1•56) ]/2 (1)

c = [17.208 ± √ (296.115 - 224) ]/2

c = 8.604 ± 4.246

To have the greater perimeter, we need the larger value of c, thus we will use the positive sign and ignore the negative one;

Thus,

c = 8.604 + 4.246 = 12.85