missing angles and sides for a triangle?

Question

I need help finding the missing side using the law of sines,

 

a=42 C=48 and C=12

Answer 1

Hi Chyna, if you mean you know side a = 42, side c = 48, and angle C, then the law of sines says:

 

a / sin A = b / sin B = c / sin C, we can drop b / sin B since it is not used.

 

42 / sin A = 48 / sin 12

 

Solve for sin A:

 

sin A = (42 / 48) * sin 12

 

sin A ≈ .182

 

Inverse sin A ≈ 10.5 degrees

 

Angle A ≈ 10.5 degrees

 

Angle B = 180 - (12 + 10.5) = 157.5 degrees.

 

Use the law of sines again to find side B.

 

c / sin C = b / sin B

 

Substitute:

 

48 / sin 12 = b / sin 157.5

 

Solve for b:

 

b = (48 * sin 157.5) / sin 12

 

b ≈ 88.35

 

The three sides are a = 42, b = 88.35, and c = 48.

 

The three angles are A = 10.5, B = 157.5, and C = 12.

 

Questions?