1. 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: c 2 = a 2 +b 2 – 2abcos C Other two sides Opposite side and angle A B C c ab

3. Law of cosines: c 2 = a 2 +b 2 – 2abcos C Finding a Missing Side Length 36 o 45 m 52 m x 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 36 o 45 52 x

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

6. Two 11-cm radii of a circle form a central angle measuring 115 o. What is the length of the chord connecting the two radii? Draw and label a picture 11 115 x 2 = 11 2 +11 2 – 2(11)(11)cos(115) x 2 = 344.27 x = 18.6 cm Example 3

7. Finding Missing Angle Measures Q E 225 250 175 D 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. D Q E 225 250 175 Start with the side across from the angle you are looking for You must solve this in steps! - 81250 -78750.2381=cosQ  Q = 76.2 o Last step is inverse (you are looking for an angle) Use cos  (.2381) CLT Undo +/- Undo ×/÷ Example 4: Find  Q

9. 51 70 62 A C B 1. Find the largest angle first (remember, the largest angle is across from the largest side) 2. Find the smallest using law of sines 76 o 3.Find the last angle by subtracting the other two from 180  C =180 – (76+45)= 59° 45° 59° CLT Undo +/- Undo ×/÷ Use cos  (.2443) Cross multiply!! Example 5: Find all of the missing angles

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

11. Homework: Law of Cosines Worksheet