Law of Cosines If you do not have

Law of cosines: c 2 = a 2+b 2 – 2 abcos C Other

Law of cosines: c 2 = a 2+b 2 – 2 abcos C Finding

Example 1 Step 1: Step 2: Step 3: Step 4: identify the opposite side/angle

Example 2 22 70 o 31 x I must see this step on your

Example 3 Two 11 -cm radii of a circle form a central angle measuring

Finding Missing Angle Measures D 250 175 Q 225 E Note: When given SSS,

Example 4: Find Q You must solve this in steps! Start with the side

Example 5: Find all of the missing angles 1. Find the largest angle first

Example 6 The diagonals of a parallelogram are 60 in and 70 in and

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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!

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

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

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

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

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 x 2 = 112 +112 – 2(11)cos(115) 11 115 11 x 2= 344. 27 x = 18. 6 cm

Finding Missing Angle Measures D 250 175 Q 225 E 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!

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 Q 225 -81250 E Last step is inverse (you are looking for an angle) -81250 -78750 Undo +/- -78750 Undo ×/÷ . 2381=cos. Q Use cos (. 2381) Q = 76. 2 o

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

Example 6 The diagonals of a parallelogram are 60 in and 70 in 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 70 35 60 64 o 30 x

Homework: Law of Cosines Worksheet