6.2 Law of Cosines

​6.2 Law of Cosines

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Multiple Choice

Which of the following formulas shows the Law of Cosines? #4

• c² = a² + b² - 4ac + cosA

• c² = a² - b² - 2abcosC

• c² = a² + b² - 2abcosC

• (cos A)/a = (cos B)/b

Multiple Choice

What are the possible criteria for the Law of Cosines? #5

• SSA, SSS

• SSA, ASA

• SSS, SAS

• AAS, ASA

Multiple Choice

Find the missing side. #10

• 15.9 in.

• 22.8 in.

• 19.2 in.

• 521.1 in.

Multiple Choice

Which would you use to find a missing angle? #13

• $$\cos\ A\ =\ \frac{b^2-a^2-c^2}{2ba}$$  

• $$\cos\ A\ =\ \frac{a^2-b^2-c^2}{-2bc}$$  

• $$\cos\ A\ =\ \frac{a^2-b^2-a^2}{4ba}$$  

• $$\sin\ A\ =\ \frac{a^2-b^2-c^2}{2bc}$$  

Multiple Choice

What is the correct set up to find angle H?

 #11

•   $$\cos\ H\ =\ \frac{11^2-13^2-15^2}{4\left(11\right)\left(15\right)}$$  

• $$\cos\ H\ =\ \frac{11^2+13^2+15^2}{2\left(13\right)\left(15\right)}$$   

•   $$\cos\ H\ =\ \frac{11^2-13^2-15^2}{-2\left(13\right)\left(15\right)}$$  

• $$H^2\ =\ 11^2+13^2+15^2-2\left(13\right)\left(15\right)\cos11$$   

Multiple Choice

$$m\angle H=$$  #6

• $$44.1\degree$$  

• $$44.6\degree$$  

• $$45.2$$  

• $$45.6\degree$$  

Fill in the Blanks

#3

Multiple Choice

Use the angle formula from the Law of Cosines to find m<C. #16

• A

• B

• C

• D

Multiple Choice

Use the angle formula from the Law of Cosines to find angle Z. #15

• 20.145 degrees

• 71.232 degrees

• 51.055 degrees

• 57.713 degrees

Multiple Select

Which of the following problems should have its solution started with the Law of Cosines. Select ALL that apply. #25

• Given: side a, side b, side c

• Given: side b, side c, angle C

• Given: side a, side c, angle B

• Given: side c, angle A, angle B

Multiple Choice

All of the following sets of given information should have their solutions started with the Law of Cosines EXCEPT. #26

• given: side a, side b, side c

• given: side a, side c, angle B

• given: side c, angle A, angle B

• given: side b, side c, angle A

Multiple Select

For Triangle ABC, which of the following applies? #32

• $$\cos A=\frac{b^2-c^2+a^2}{2bc}$$

• $$\cos A=\frac{b^2+c^2-a^2}{2bc}$$

• $$\cos B=\frac{a^2+c^2-b^2}{2ac}$$

• $$\cos C=\frac{b^2+a^2-c^2}{2ba}$$

• none of these

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Multiple Choice

Which of the following is Heron's Formula for finding area of triangle? #38

• $$A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$$  

• $$A=\sqrt{s\left(s+a\right)\left(s+b\right)\left(s+c\right)}$$  

• $$A=\sqrt{\left(s+a\right)\left(s+b\right)\left(s+c\right)}$$  

• $$A=\sqrt{s\left(s\times a\right)\left(s\times b\right)\left(s\times c\right)}$$  

Multiple Choice

What is the semi-perimeter? #37

• 1/2 of the actual perimeter

• A circular object rotated 90 degrees on its axis

• My dog's name

• The distance around a semi truck multiplied by the square root of the perimeter

Multiple Choice

Using Heron's Formula, find the Area. #39

• 56

• 28

• 24.2

• 104.4