(1)

Step 1:

Length of side of the triangle is .

Angles of the triangle are .

The third angle is .

Step 2:

Find the length of side .

Apply sines law: .

Consider .

Substitute and .

Solution:

(2)

Side of the triangle is .

Angle of the triangle is .

Law of sine:

Either of the angles or any one of the side is needed to apply law of sines.

For an example, consider

To find the value of angle , side has to be known.

(9)

Step 1:

Length of side of the triangle is .

Angles of the triangle are .

Find the length of side .

Apply sines law: .

Consider .

Substitute , .

Solution:

Observe the figure:

The three sides of the triangle are known forming the case of SSS triangle.

The Law of sines cannot be applied to SSS triangle.

Therefore, Law of sines cannot be applied.

Law of sines for the triangle: .