Determine the number of triangles with the given parts and solve the triangle

Question

If someone could help me out with these three it would be so helpful, I can't figure them out, thank you in advance!

Answer 1

(1)

Step 1:

The sides and angle of the triangle

Law of sines

Find .

Substitute in the law of sines.

Find .

Substitute in

Find .

Substitute in law of sines.

Solution:

The number of triangles with parts are

Answer 2

(3)

Step 1:

The sides and angle of the triangle

Law of  cosine rule :

Substitute in the cosine rule.

Find .

Law of sines

Find .

Substitute in the law of sines.

Find .

Substitute in

Solution:

The number of triangles remaining parts are

Answer 3

(2)

Step 1:

The vector is

Find the magnitude.

Magnitude of the vector

Substitute in the formula of magnitude.

Magnitude of the vector

Find the Direction.

Direction of the vector

Substitute in the direction formula.

Direction of the vector

Solution:

Magnitude of the vector

Direction of the vector