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angle A=29.8, side a=28.6, side b 35.8. Find two triangles.

 Apr 12, 2019
 #8
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sin A / a  =  sin B / b

sin (29.8)  / 28.6  =  sin B / 35.8

35.8 sin (29.8) / 28.6 =  sin B

arcsin  (35.8 sin (29.8) / 28.6)  = B ≈  38.5°

So....C = 180 - 29.8 - 39.5  = 110.7°

And

a/sin A = c / sin C

28.6 / sin 29.8 = c /  sin 110.7

28.6sin 110.7 / sin 29.8  =   = 53.8

 

So   1st triangle 

A = 29.8  B = 38.5 C = 110.7

a = 28.6  b =35.8   c = 53.8

 

Subtract  38.5 from 180  = 141.5°   = B

Add this to A  = 171.3 < 180   so we have two triangles

And angle C = 180 - 171.3 = 8.7°

So using the Law of Sines again to find c , we have

a /sin A = c / sin C

28.6 / sin 29.8 = c / sin 8.7

28.6sin 8.7 / sin 29.8 = c = 8.7

 

So  ...in the second triangle

A = 29.8   B = 141.5  C = 8.7

a = 28.6   b =  35.8    c = 8.7

 

 

 

 

 

cool cool cool

 Apr 12, 2019

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