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