ANSWER
[tex]B = 27.8 \degree[/tex]
EXPLANATION
The law of cosine is given by the formula:
[tex] {b}^{2} = {a}^{2} + {c}^{2} - 2bc \cos(B) [/tex]
From the diagram,
a=17, b=8, c=16
We substitute the given values into the formula to obtain:
[tex] {8}^{2} = {17}^{2} + {16}^{2} - 2(17)(16)\cos(B) [/tex]
[tex]64 = 289+ 256- 544\cos(B) [/tex]
[tex]64 = 545- 544\cos(B) [/tex]
[tex]64 - 545 = - 544\cos(B) [/tex]
[tex] - 481 = - 544\cos(B) [/tex]
[tex] \frac{ - 481}{ - 544} = \cos(B) [/tex]
[tex]cos(B) = 0.88419[/tex]
[tex]B = \cos ^{ - 1} (0.88419)[/tex]
[tex]B = 27.8 \degree[/tex]
