Question

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

Find x. (accurate to 3 significant figures)
The value of x = .

Answer 1

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.

Answer 2

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