Question

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

B = 126°, c = 7, b = 12

Answer 1

We are given 2 sides and a NON - included angle.
The Law of sines cannot be used because we need two angles.
The Law of Cosines cannot be used because we need an INCLUDED angle.

When we are given a triangle with side 'b' AND its opposite Angle 'B' and side 'c', there can be no, one or two solutions.

In this case, when the side opposite the given angle is greater than the other side (12 is greater than 7) then there is one solution.

Answer 2

Using law of sines triangle can be solved.

Explanation:

Given that side b and angle opposite to B.

Hence law of sines can be used. Since 3 measurements are given, they are sufficient to solve for the triangle

We have

sin C =csinB/b=7sin126/12

C=28.16 degrees

A=180-(B+C)=25.84

Side a= cSinA/sinC =6.47

Thus using law of sines for triangles the triangle is solved by finding out all the sides and also angles