Question 1109653
In triangle ABC a=4 b=11 and c=8 find m&#8736;B?<pre>
{{{drawing(400,1680/13,-1,12,-1,3.2,

triangle(0,0,11,0,73/22,2.233756796),
locate(.6,1.5,a=4),locate(6.4,1.8,c=8),locate(4.4,0,b=11),
locate(0,0,C), locate(11,0,A), locate(3.2,2.7,B) )}}}

For the SSS case, we use the law of cosines:

 b² = a² + c² - 2&#8729;a&#8729;c&#8729;cos(B)

11² = 4² + 8² - 2&#8729;4&#8729;8&#8729;cos(B)
121 = 16 + 64 - 64&#8729;cos(B)
121 = 80 - 64&#8729;cos(B)
 41 = -64&#8729;cos(B)
{{{-41/64}}} = cos(B)

Use inverse cosine key on your calculator

B = 129.83844°

Ewin</pre>