Module 6 Lesson 3
Check Your Knowledge
Match each situation to the “Process necessary to find the area of the
triangle” given each triangle’s information.
Situation
1. Three sides (SSS)
Process necessary to find the area
of the triangle of finding the area
a. First, find the 3rd angle using
subtraction. Then use the
formula.
K
1 2 sin A  sin B
c
2
sin C
2. Two sides and the angle in
between them (SAS)
b. First, find 2nd angle using Law
of Sines. Then, find 3rd angle
using subtraction. Last, use the
1 sin A  sin B
formula K  c 2
2
sin C
3.Two sides and an angle NOT in
between them (SSA)
c. First, calculate “s” then use the
formula K  s( s  a)( s  b)( s  c)
4. Two angles and the side in
between them (ASA)
d. Use the formula K 
5. Two angles and the side NOT in
between them (AAS)
1
bc sin A
2
with the given information.
e. First, find the 3rd angle using
subtraction. Then use the
formula.
1 sin A  sin B
K  c2
2
sin C
Answer Key:
1. C
Feedback: Your notes explain when you are given 3 sides you can
calculate the “s” value and use Hero’s formula.
2. D
Feedback: Your notes explain when “b” and “c” are sides and “A” is the
1
angle between the sides you can use the formula K  bc sin A and
2
solve for the area without multiple calculations.
3. B
Feedback: When given 2 sides and the angle not in between them, use
the Law of Sines and then subtraction to find the other 2 angles to use
1 sin A  sin B
the formula K  c 2
2
sin C
4. E or A
Feedback: When given 2 angles to start with, use subtraction to find
1 sin A  sin B
the 3rd angle and use the formula K  c 2
2
sin C
5. A or E
Feedback: When given 2 angles to start with, use subtraction to find
1 sin A  sin B
the 3rd angle and use the formula K  c 2
2
sin C
Another chart with the answers matched together.
Three sides (SSS)
First, calculate “s” then use the
formula K  s( s  a)( s  b)( s  c)
Two sides and the angle in
between them (SAS)
Use the formula K 
Two sides and an angle NOT in
between them (SSA)
First, find 2nd angle using Law of
Sines
1
bc sin A with
2
the given information.
Then, find 3rd angle using
Subtraction
Last, use the formula
1 sin A  sin B
K  c2
2
sin C
Two angles and the side in
between them (ASA)
First, find the 3rd angle using
subtraction. Then use the
formula.
1 sin A  sin B
K  c2
2
sin C
Two angles and the side NOT in
between them (AAS)
First, find the 3rd angle using
subtraction. Then use the
formula.
K
1 2 sin A  sin B
c
2
sin C