1. SOH CAH TOA only works in right triangles!
Law of Cosines
If you do not have a right triangle you use Law of Sines or Law of cosines.
SOH CAH TOA only works in right triangles!

2. Law of cosines: c2 = a2+b2 – 2abcos C
Other two sides C
Opposite side and angle b a A B c

3. Law of cosines: c2 = a2+b2 – 2abcos C
Finding a Missing Side Length
45 m x
36o
52 m
Step 1: Identify the opposite side/angle
Step 2: Plug into law of cosines formula
Step 3: Solve using your calculator
Step 4: Last step is to take the square root
To use law of cosines to find a side you must have SAS

4. Example 1 Step 1: identify the opposite side/angle
Step 2: plug into law of cosines formula
Step 3: solve using your calc
Step 4: last step is to take the square root 45 x
36o 52

5. I must see this step on your homework for credit!
Example 2
70o 22 31
I must see this step on your homework for credit! x

6. Example 3
Two 11-cm radii of a circle form a central angle measuring 115o. What is the length of the chord connecting the two radii?
Draw and label a picture
x2 = – 2(11)(11)cos(115)
x2=
x = 18.6 cm 11
115 11

7. Finding Missing Angle Measures
250
175 E Q
225
Note:
When given SSS, it is always best to solve for either your biggest or smallest angle first so you have a reference point when finding the other two angles!

8. Last step is inverse (you are looking for an angle)
Example 4: Find Q
You must solve this in steps!
Start with the side across from the angle you are looking for D
CLT
250
175
-81250
-81250
Undo +/-
-78750 E Q
-78750
Undo ×/÷
225
.2381=cosQ
Last step is inverse (you are looking for an angle)
Use cos(.2381)
Q = 76.2o

9. C 70 B A 62 Example 5: Find all of the missing angles 51
1. Find the largest angle first (remember, the largest angle is across from the largest side) C 70
59° 51
CLT
Undo +/-
76o
45° B A 62
Undo ×/÷
2. Find the smallest using law of sines
Use cos(.2443)
Find the last angle by subtracting the other two from 180
C =180 – (76+45)= 59°
Cross multiply!!

10. Example 6
The diagonals of a parallelogram are 60 in and 70in and intersect at an angle measuring 64o. Find the length of the shorter side of the parallelogram. Round to the nearest tenth place.
Draw a picture 70 35 60 x
64o 30

11. Law of Cosines Worksheet
Homework:
Law of Cosines Worksheet