Use the Law of Sines to solve the triangle. Round your answers to two decimal places.

Question

 (Let b = 6.4.)

B=   °

a=

c=

Answer 1

The Law of Sines formula is: SinA/a = SinB/b = SinC/c

If angles A and C are both 16 degrees, then we know angle B = 180 - 16 - 16 = 148 degrees (this picture is deceiving as angle C appears obtuse and angle B appears acute but that's clearly not the case...also, this is an isosceles triangle based on the angle measures but it doesn't look even close to isosceles). We know angle C is congruent to angle A based on the arc in the picture.

To find a, use the Law of Sines: (sin16)/a = (sin 148)/6.4

Now, cross multiply --> a(sin 148) = 6.4(sin 16)

Now, solve for a --> a = (6.4 * sin16) / sin 148

a = 3.33

Side c must equal side a because their opposite angles are congruent. Thus, c = 3.33