Question

I have X, I just need Y.

Answer 1

I'm getting x = 9.3223 which rounds to 9.32. Nice work.

Once you know the value of x, you can use the law of sines to find the value of y

sin(A)/a = sin(B)/b

sin(y)/7 = sin(70)/x

sin(y)/7 = sin(70)/9.3223

sin(y) = 7*(sin(70)/9.3223)

sin(y) = 0.70560358983312

y = arcsin(0.70560358983312)

y = 44.8783278056846

y = 44.88 approximately

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If you must use the law of cosines, then here's how you could do it

c^2 = a^2 + b^2 - 2*a*b*cos(C)

7^2 = x^2 + 9^2 - 2*x*9*cos(y)

7^2 = (9.3223)^2 + 9^2 - 2*9.3223*9*cos(y)

49 = 86.90527729+81-167.8014cos(y)

49 = 167.90527729-167.8014cos(y)

-167.8014cos(y) = 49-167.90527729

-167.8014cos(y) = -118.90527729

cos(y) = -118.90527729/(-167.8014)

cos(y) = 0.708607182598

y = arccos(0.708607182598)

y = 44.8782954209662 ... this is slightly different from before due to rounding error

y = 44.88 approximately