My teacher has reached a new low.?

So... what's your question?

The area of a triangle is ½Bh, where B is the base and h is the height. You can often find the height by using trigonometry. If you only have the sides, you can even use Heron's formula.

The law of cosines is c² = a² + b² − 2abcos(C), where a, b, c are side lengths and C is the angle opposite side c.

I can sympathize but you'll need to put up some more specific questions if we're to send any practical help.

The cosine law relates to a triangle. If you label a triangle ABC and the side opposite the angle labelled A is a , B is b , C is c then

a^2 = b^2 + c^2 - 2bccosA.

Its a general rule and works for any triangle. So if they give you 3 bits you can find the others. Is that what the assignments are about.

There is another formula for the area of a triangle which is 1/2 ab sinC where you've labelled the triangle as above.

law of cosines and sines is triganometry but has some geometric value. Law of cosines is c squares= a^2 + b^2 + 2(a)(b)cosC

the area of a triangle if you know one angle and two sides is 1/2(a)(b)sinC

Perhaps she is trying to get the class to be involved in independent study and show some ability to learn on their own. She is probably going to teach it in class after.

If ever you do not understand an assignment, always take a moment to speak with the teacher and ask her to clarify.