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4 years ago

Find all the missing elements. A=109 C=13 b=6 B=? a=? c=?

Mathematics

1 answer:

sasho [114]4 years ago

7 0

Answer:

B = 58°
a = 6.6896
c = 1.5915

Step-by-step explanation:

Given two angles and the side between them, the first step must be to find the value of the third angle, the one opposite the given side. It will be ...

B = 180° -A -C = 180° -109° -13° = 58°

Using this information and the Law of Sines, you can find the remaining sides.

a/sin(A) = b/sin(B) = c/sin(C)

Then the missing sides are ...

a = b(sin(A)/sin(B)) = 6(sin(109°)/sin(58°)) ≈ 6.6896

c = b(sin(C)/sin(B)) = 6(sin(13°)/sin(58°)) ≈ 1.5915

The missing measures are ...

B = 58°

a = 6.6896

c = 1.5915

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