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1. What is the length of JK, to the nearest tenth of a millimeter?

Options: 4.5, 5.6, 8.3, 19.9 mm

 

2. What is the length of EF? Answer in decimal form and round only final answer to the nearest tenth.

Guest Apr 14, 2017

Best Answer 

 #1
avatar+7155 
+3

For these problems, we can use the law of cosines:

c2 = a2 + b2 — 2abcosC

 

1.

c = JK

a = 3

b = 5

C = 62º

 

Plug these values into the law of cosines.

(JK)2 = 32 + 52 - 2(3)(5)cos 62

(JK)2 = 9 + 25 - 30cos 62

(JK)2 = 34 - 30cos 62

JK = \(+\sqrt{34 - 30cos 62} \approx4.5\text{ mm}\)

 

 

2.

c = EF

a = 6

b = 11

C = 40º

 

Plug these values into the law of cosines.

(EF)2 = 62 + 112 - 2(6)(11)cos 40

(EF)2 = 36 + 121 - 132cos 40

(EF)2 = 157 - 132cos 40

EF = \(+\sqrt{157 - 132cos 40} \approx7.5\text{ ft}\)

hectictar  Apr 14, 2017
 #1
avatar+7155 
+3
Best Answer

For these problems, we can use the law of cosines:

c2 = a2 + b2 — 2abcosC

 

1.

c = JK

a = 3

b = 5

C = 62º

 

Plug these values into the law of cosines.

(JK)2 = 32 + 52 - 2(3)(5)cos 62

(JK)2 = 9 + 25 - 30cos 62

(JK)2 = 34 - 30cos 62

JK = \(+\sqrt{34 - 30cos 62} \approx4.5\text{ mm}\)

 

 

2.

c = EF

a = 6

b = 11

C = 40º

 

Plug these values into the law of cosines.

(EF)2 = 62 + 112 - 2(6)(11)cos 40

(EF)2 = 36 + 121 - 132cos 40

(EF)2 = 157 - 132cos 40

EF = \(+\sqrt{157 - 132cos 40} \approx7.5\text{ ft}\)

hectictar  Apr 14, 2017

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