# Law of Cosines Lesson 4 2 Whos Law

• Slides: 15

Law of Cosines Lesson 4. 2

Who's Law Is It, Anyway? ¡ Murphy's Law: l ¡ Anything that can possibly go wrong, will go wrong (at the worst possible moment). Cole's Law ? ? l Finely chopped cabbage 2

Solving an SAS Triangle ¡ The Law of Sines was good for l l l ¡ ASA AAS SSA - two angles and the included side - two angles and any side - two sides and an opposite angle (being aware of possible ambiguity) Why would the Law of Sines not work for an SAS triangle? No side opposite from any angle to get the ratio 15 26° 12. 5 3

Deriving the Law of Cosines C b ¡ Write an equation using Pythagorean theorem for shaded triangle. h k a c-k A B c 4

Law of Cosines ¡ Similarly ¡ Note the pattern 5

Applying the Cosine Law ¡ Now use it to solve the triangle we started with C 15 ¡ Label sides and angles l Side c first A 26° c 12. 5 B 6

Applying the Cosine Law C 15 A ¡ 26° c = 6. 65 12. 5 B Now calculate the angles l use and solve for B 7

Applying the Cosine Law C 15 A ¡ 26° c = 6. 65 12. 5 B The remaining angle determined by subtraction l 180 – 93. 75 – 26 = 60. 25 Experiment with Cosine Law Spreadsheet 8

Wing Span C The leading edge of each wing of the B-2 Stealth Bomber measures 105. 6 feet A in length. The angle between the wing's leading edges is 109. 05°. What is the wing span (the distance from A to C)? ¡ Hint … use the law of cosines! ¡ 9

Assignment A Lesson 4. 2 A ¡ Page 308 ¡ Exercises 1 – 27 odd, and 41 - 51 odd ¡ 10

Using the Cosine Law to Find Area ¡ ¡ Recall that We can use the value for h to determine the area C b h a A B c 11

Using the Cosine Law to Find Area ¡ We can find the area knowing two sides and the included angle C b A ¡ a c B Note the pattern 12

Try It Out ¡ Determine the area of these triangles 42. 8° 17. 9 12 127° 24 76. 3° 13

Cost of a Lot ¡ An industrial piece of real estate is priced at \$4. 15 per square foot. Find, to the nearest \$1000, the cost of a triangular lot measuring 324 feet by 516 feet by 412 feet. 32 2 4 41 516 14

Assignment B Lesson 4. 2 B ¡ Page 309 ¡ Exercises 29 – 39 odd and 53 – 61 odd ¡ 15