Find all solutions for a triangle with a=140°,b=10, and a=3

your triangle is made of big circles on a sphere. In spherical trigonometry the law of sines is [Law of sines - Wikipedia]

sinA

sina

=

sinB

sinb

=

sinC

sinc

sin⁡Asin⁡a=sin⁡Bsin⁡b=sin⁡Csin⁡c

Your triangle is in the case 5,  

aAB

aAB

, from [Spherical trigonometry - Wikipedia]. In this case you get  

b

b

by the law of sines:

sinb=

sinBsina

sinA

sin⁡b=sin⁡Bsin⁡asin⁡A

and apply case 7, which is solved as explained in the wikipedia page using Napier’s analogies.

else

it was a mistake and your triangle is in Euclidean geometry. The law of sines is then

sinA

a

=

sinB

b

=

sinC

c

sin⁡Aa=sin⁡Bb=sin⁡Cc

You find  

C=

180

∘

−A−B

C=180∘−A−B

, then apply the law of sines to find  

b

b

and  

c

c

.

Step-by-step explanation:

if im undersanding the question correctly, its organized from 10

step-by-step explanation:

step-by-step explanation: