Question

Need help! Law of cosines...find b round to the nearest tenth please

Answer 1

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`