1. Law of Sines Goal: To solve triangles which aren’t necessarily
right triangles ( find all sides & angles) C b a A B c or

2. : 0≤sinØ≤1 when 0˚≤Ø≤180˚
: There may be no answers, 1 answer, or
2 answers. (There are 2 angles--1 acute,
1 obtuse--that have the same sine.)
: If there are 2 angles given, you can easily
find the 3rd angle (the 3 angles of a triangle
add up to 180˚).

3. : To change the decimal part of degrees
to minutes, multiply the decimal part by
60. (._ _ means ‘hundredths’…we want
‘minutes’, which is 60ths.)
: If the given angle Ø>90˚and there exists
a solution, then there exists only 1 solution.
: In order to use this formula, you must
know at least 1 angle and its corresponding
side OR 2 angles and 1 side.

4. : We found C by taking 180-(25˚26’+78˚). Ex:
Determine the number of possible solutions. If a solution exists, solve
the triangle.
1. a=13.7, A=25˚26’, B=78˚
: We found C by taking
180-(25˚26’+78˚).
A= 25˚26’ a= 13.7
B= 78˚ b=
C= c=
31.2
76˚34’
31.0

5. : We need not go any farther. Ex: 2. a=33, A=132˚, b=50 A=132˚ a=33
Determine the number of possible solutions. If a solution exists, solve
the triangle.
2. a=33, A=132˚, b=50
: We need not go any
farther.
A=132˚ a=33
B= b=50
C= c=

6. OR : We found C by taking 180-(sum of A+B). Ex: 1. a=125, A=25˚, b=150
Determine the number of possible solutions. If a solution exists, solve
the triangle.
1. a=125, A=25˚, b=150 OR
A= 25˚ a=125
B= b=150
C= c=
: We found C by taking
180-(sum of A+B).
30˚28’
or 149˚32’
124˚32’
or 5˚28’
243.7
or 28.2’