Determine whether the given information results in one triangle, two triangles, or no triangle at all.

Question

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.

a = 3,    b = 2,     A = 50^o

Answer 1

Step 1:

The sides of a triangle are and .

The angle of triangle .

To solve the triangle, use Law of Sines.

Using law of sines formula  .

Step 2:

Consider .

Substitute , and in sine formula.

The angle .

 .

Therefore, is satisfies.

The given information results in one triangle.

Step 3:

The sum of three angles in a triangle,

To find other side, by using law of sines formula .
Consider .

Substitute , and in sine formula.

Solution:

The given information results one triangle.

The triangle side is 

The angles of triangle are