College Algebra & Trigonometry, 2018a

11.1. THE LAW OF SINES 473
To put this in the form in which the Law of Sines is normally stated, we can divide
on both sides of the previous expression by ab:
a sin B = b sin A
a sin B
ab
= b sin A
ab
sin B
b
= sin A
a
A similar process will show that sin C
c
is equivalent to sin B
b
and sin A
a
. The diagram
we derived this from used an acute triangle in which all the angles were less than
90 ◦ . The process to show that this is true for an obtuse triangle (which has one
angle larger than 90 ◦ ) is relatively simple and is left to the reader to discover or
look up in another resource.
The Law of Sines
sin A
a
=sin B
b
= sin C
c
Sometimes it is handy to set up a problem with the side lengths in the numerator:
The Law of Sines
a
sin A = b
sin B = c
sin C
Example 1
Solve the triangle. Round side lengths to the nearest 100 th .
a
b
45 ◦ 95 ◦ 5
A