Given the triangle ABC c=8, ∠b=30°, b=3find all the other missing values Please show the complete solution with an explanation. |

This is the SSA case: the possibilities include no solution, exactly one solution, or two solutions. As sciencesolve's solution shows, there is no solution.

An alternative to the Law of Sines in this case is to use the Law of Cosines -- the advantage is in the case where there are two solutions, as both solutions will be provided.

Let BC=a. Then applying the Law of Cosines using angle B we get:

`b^2=a^2+c^2-(a)(c)cosB`

`3^2=a^2+8^2-(8)(a)cos30^(circ)`

`9=a^2+64-8a(sqrt(3)/2)`

`a^2-4sqrt(3)a+55=0`

Applying the quadratic formula we get:

`a=(4sqrt(3)+-sqrt(48-4(1)(55)))/2` . Since the discriminant is negative, there are no real solutions. Thus no triangle can be formed with the given attributes.