1 Answer

Eladv · Answer 1 · 2020-12-26T13:10:01+0000

ANSWER

$B = 27.8 \degree$

Step-by-step explanation

The law of cosine is given by the formula:

${b}^(2) = {a}^(2) + {c}^(2) - 2bc \cos(B)$

From the diagram,

a=17, b=8, c=16

We substitute the given values into the formula to obtain:

${8}^(2) = {17}^(2) + {16}^(2) - 2(17)(16)\cos(B)$

$64 = 289+ 256- 544\cos(B)$

$64 = 545- 544\cos(B)$

$64 - 545 = - 544\cos(B)$

$- 481 = - 544\cos(B)$

$( - 481)/( - 544) = \cos(B)$

cos(B) = 0.88419

$B = \cos ^( - 1) (0.88419)$

$B = 27.8 \degree$

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