1. Warm Up 1. Find the area: Round to the nearest meter. 33m 39m 61 A B C 2. Find the missing angle measure: Round to the nearest tenth. 34ft 48ft 44 x 3. Find the missing side length: Round to the nearest tenth. 40cm n 59 46 563m 2 78.7 0 47.7 cm

2. 12.4 Law of Cosines – part 1  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

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

4. 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 calc Step 4: Last step is to take the square root To use law of cosines to find a side you must have SAS

5. Example 1: Find the length of x 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

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

7. Example 3: 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

8. Law of cosine: c 2 = a 2 +b 2 – 2abcos C Finding Missing Angle Measures Q E 225 250 175 D

9. Example 1: Find  Q D Q E 20 25 17 Start with the side across from the angle you are looking for You must solve in steps -689 -680.0941=cosQ  Q = 84.6 o Last step is inverse (you are looking for an angle) Use cos  (.0941) CLT Undo +/- Undo ×/÷

10. Find all missing angles- round to the nearest degree 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° Given only the sides use Law of Cosines to find an angle…This is a special case when solving for an angle. Start with the largest side then find the smallest angle. Next, find the smallest angle 45° 59° CLT Undo +/- Undo ×/÷ Use cos  (.2443) Cross multiply!!

11. Example 3: 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

12. Homework: WS: 12.4 Summary: What information do you need to use Law of Cosines?