The first three formulas refer to the triangle ABC, with sides a = BC, b = AC, c = AB:

I. Area formula:

Area = 1/2 ab sin(C)

Note that when C is a right angle, then sin(C) = 1, so this formula says Area = 1/2 ab, or 1/2 base times height. A possible
application is to find a formula for the area of a quadrilateral.

II. Law of cosines:

c^2 = a^2 + b^2 - 2ab cos(C).

Note that when C is a right angle, then cos(C) = 0, so this formula says c^2 = a^2 + b^2, which is just the Pythagorean
theorem. A possible topic for discussion is to interpret this formula geometrically, generalizing the interpretation of the
Pythagorean theorem using squares on the three sides of the triangle. Another might be a formula for the length of a side
of a quadrilateral, in terms of the other three sides and the two angles determined by these three sides.

III. Law of sines:

a/sin(A) = b/sin(B) = c/sin(C).

Note that when C is a right angle, then these equations just say that a/sin(A) = b/sin(B) = c, or sin(A) = a/c and sin(B) =
b/c, which are just the definitions of sin(A) and sin(B). A possible topic for discussion is that these numbers are equal to
twice the circumradius of the triangle ABC.

IV. Addition formulas:

sin(a + b) = sin a cos b + cos a sin b

cos(a + b) = cos a cos b - sin a sin b

Possible topics for discussion are the relation of these formulas to the multiplication of complex numbers, or their relation
to the multiplication of rotation matrices.

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