Chyna O.

asked • 04/20/16# missing angles and sides for a triangle?

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

a=42 C=48 and C=12

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## 1 Expert Answer

Don L. answered • 04/20/16

Tutor

5
(12)
Fifteen years teaching and tutoring basic math skills and algebra

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.

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04/20/16