Question

Use the Law of Cosines to find the side length c. Use the Law of Sines to find angle B of the triangle in the previous problem. Photo is attached.

Thank you for your help I appreciate it.

Answer 1

Explanation:

Let a = 8 and b = 11. Using the law of cosines, we can write

`c^2 = a^2 + b^2 - 2abcos(c)`

`\:\:\:\:=(8)^2 + (11)^2 - 2(8)(11)cos(37) = 44.44`

`c = 6.67`

Now we're going to use the sine to find
`\angle{B}:`

`(sin(B))/(b) = (sin(37))/(c)`

or

`sin(B) =\left((b)/(c)\right)sin(37) = 0.992`

or

`B = \sin^(-1)(0.992) = 83.0°`