In ∆abc, c=5.4, a= 3.3 and m less than a =20. what are the possible approximate length of b? use the laws of sines to find answer 2.0 units and 4.6 units 2.1 units and 8.7 units 2.3 units and 7.8 units 2.6 units and 6.6 units

The Law of Sines tells you

... sin(C)/c = sin(A)/a

... sin(C) = c·sin(A)/a . . . . multiply by c

... C = arcsin(c·sin(A)/a) . . take the inverse sine

Then

... sin(B)/b = sin(A)/a . . . . law of sines again

... b = a·sin(B)/sin(A) . . . . multiply by a·b/sin(A)

where B = 180° - A - C = 160° - C . . . . . . sum of angles in a triangle is 180°

Filling in the given values, we get

... C = arcsin(5.4·sin(20°)/3.3) ≈ 34.033° or 145.967°

Then

... B = 125.967° or 14.033°

and

... b = 3.3/sin(20°)·sin(125.967°) or 3.3/sin(20°)·sin(14.033°)

... b = 7.8 or 2.3 . . . units

The appropriate choice is

... 2.3 units and 7.8 units

the answer will be