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### Law of Cosines

Lesson 4.2

Who's Law Is It, Anyway?

- Murphy's Law:
- Anything that can possibly go wrong, will go wrong (at the worst possible moment).

- Cole's Law ??
- Finely chopped cabbage

Solving an SAS Triangle

- The Law of Sines was good for
- ASA - two angles and the included side
- AAS - two angles and any side
- SSA - two sides and an opposite angle (being aware of possible ambiguity)

- Why would the Law of Sines not work for an SAS triangle?

15

26°

No side opposite from any angle to get the ratio

12.5

Deriving the Law of Cosines

C

- Write an equationusing Pythagorean theorem for shaded triangle.

b h a

k c - k

A B

c

Law of Cosines

- Similarly
- Note the pattern

Applying the Cosine Law

- Now use it to solve the triangle we started with
- Label sidesand angles
- Side c first

C

15

26°

12.5

A B

c

Applying the Cosine Law

- The remaining angledetermined by subtraction
- 180 – 93.75 – 26 = 60.25

C

15

26°

12.5

A B

c = 6.65

Experiment with Cosine Law Spreadsheet

Wing Span

C

- The leading edge ofeach wing of theB-2 Stealth Bombermeasures 105.6 feetin 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!

A

Assignment A

- Lesson 4.2A
- Page 308
- Exercises 1 – 27 odd, and 41 - 51 odd

Using the Cosine Law to Find Area

- Recall that
- We can use the value for hto determinethe area

C

b h a

A B

c

Using the Cosine Law to Find Area

- We can find the area knowing two sides and the included angle
- Note the pattern

C

b a

A B

c

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.

324

412

516

Assignment B

- Lesson 4.2B
- Page 309
- Exercises 29 – 39 oddand 53 – 61 odd

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