Question

In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.

Answer 1

To solve the value of x we use the sine rule that states. 
a/sinA = b/sinB = c/sinC
Where a, b, and c are the opposite sides of angle A, B. and C respectively. 

x/sin60 = 7/sin80

 x =(7sin60)/sin80

    = 6.062/0.9848
    =6.155696691

To 3 significant figures the answer is 6.16 

Answer 2

Using the law of the sine we have two possibilities:
 Way 1:
 x / sine (60) = 7 / sine (80)
 Rewriting we have:
 x = (7 / sine (80)) * (sine (60))
 x = 6.16
 Way 2:
 x / sine (80) = 7 / sine (60)
 Rewriting we have:
 x = (7 / sine (60)) * (sine (80))
 x = 7.96
 Answer:
 x = 6.16
 or
 x = 7.96
 Note: it depends on the location of a and b in the triangle.