College Algebra & Trigonometry, 2018a

472 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
If we drop a perpendicular to the base of the triangle from the vertex point at ∠C,
this creates two right triangles with which we can make use of the right triangle
trigonometry covered in Chapter 1. This perpendicular would be the height of
the triangle.
C
b
h
a
A
c
B
The Law of Sines is derived from this configuration and allows us to calculate the
value of sides and angles in a triangle without a right angle, based on information
about known sides and angles. Given the right triangles in the diagram above,
we can see that:
sin B = h a
and
sin A = h b
Clearing the denominator in each fraction, we can see that:
a sin B = h
and
b sin A = h
so
a sin B = b sin A