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Warm Up 4/20

Warm Up 4/20. 1. Find the area: Round to the nearest meter. 2. Find the missing angle measure: Round to the nearest tenth. B. 78.7 0. x. 563m 2. 34ft. 33m. 44. 61. A. 39m. C. 48ft. 3. Find the missing side length: Round to the nearest tenth. n. 40cm. 47.7 cm. 46. 59.

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Warm Up 4/20

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  1. Warm Up 4/20 1. Find the area: Round to the nearest meter. 2. Find the missing angle measure: Round to the nearest tenth. B 78.70 x 563m2 34ft 33m 44 61 A 39m C 48ft 3. Find the missing side length: Round to the nearest tenth. n 40cm 47.7 cm 46 59

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

  4. 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 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 45 x 36o 52

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

  7. 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 = 112 +112 – 2(11)(11)cos(115) x2= 344.27 X = 18.6 cm 11 115 11

  8. Law of cosine: c2 = a2+b2 – 2abcos C Finding Missing Angle Measures D 250 175 E Q 225

  9. Example 1: Find Q You must solve in steps Start with the side across from the angle you are looking for D CLT 250 175 -81250 -81250 Undo +/- -78750 -78750 E Q Undo ×/÷ 225 .2381=cosQ Last step is inverse (you are looking for an angle) Use cos(.2381) Q = 76.2o

  10. Find all missing angles- round to the nearest degree 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. C 1. Find the largest angle first (remember, the largest angle is across from the largest side) 51 59° 70 CLT Undo +/- 45° 76o B A 62 Undo ×/÷ Next, find the smallest angle 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!!

  11. Example 3: • 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

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

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