5.3.3 law of cosinesblogs.4j.lane.edu/hegedus_j/files/2016/11/geo-5.3.3...sina b sinb c sinc = =...
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5.3.3 Law of Cosines
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HW Check
5-93.Nextslide
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Group Quiz Time: 11/16/17• Show your own work. Show all work.• Use your INB, pencil, eraser, scientific
calculator.• No phones out when quizzes are out• I will randomly select one quiz from each
table group. All present members of that group will receive the score earned by that quiz, so ensure your teammates would be satisfied with the work & results you have shown on your quiz.
• Place all quizzes from your table group in a stack when finished for me to collect; then, preview Lesson 5.3.3.
• If you want to access accommodations for extended time/alternative location, please write where to route your quiz, and/or Room Number & date/time where & when you will complete the quiz, such as, "➔ Rebecca ➔ Jordan," or, "Finish in Rm 704, 9/15 @ 3:35."
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Objective(s): You will use the Law of Cosines to solve triangles you were previously unable to solve with the tools you possessed.
Agenda:• Review HW (Teams)• Group Quiz (Teams)• Review LoS (Class)• Introduce LoC/Record Notes in Spiral (Class)• Lesson 5.3.3 Activity (Teams, in Spirals)
> 5-96f> 5-97> 5-98
• Record / Begin HW (Class / Individual):
5-100 to 5-105
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5-55. In a random sample of 10,000 college students, a research company found that 35.7% were involved in a club and 27.8% studied 4 or more hours per day. When they reported their findings, the research company indicated that 53.4% of college students were either involved in a club or they studied 4 or more hours per day. Given this information, what is the probability that a college student is involved in a club and studies 4 or more hours per day?
10.1% by using the Addition Rule.
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a.
b.
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h=6
A = 0.5 (24) (6) = 72 u2
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CPM
318
(LoS or L-o-S)
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Law of Sines
AASASA
SinAa
SinBb
SinCc
= =
A
B
C
a
b
c
aSinA
bSinB
cSinC
= =
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x 5
25° 50°
Law of SinesFind x.
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x 5
25° 50°
Law of SinesFind x.
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Law of Cosines (LoC)
c2 = a2 + b2 – 2ab•CosC b2 = a2 + c2 – 2ac•CosB a2 = c2 + b2 – 2cb•CosA
You can also use it to solve for an angle when you know 3 sides & solve the equation algebraically, with the final step involving inverse trig.
COPY ALL TEXT & DIAGRAMS FROM SLIDE:
SAS, SSS
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Objective:
Complete your Triangle Toolkit with the Law of Cosines.
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Direct instruct this problem
Class Work:• Read MN;• Complete 5-96 f through 5-98.
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DA = b - x
(b-x)
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a2 = x2 + y2
c2 = y2 + (b - x)2
(b-x)
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a2 = x2 + y2
c2 = y2 + (b - x)2
(b-x)
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a2 = x2 + y2
a2 – x2 = y2c2 = y2 + (b - x)2
c2 – (b – x)2 = y2
a2 – x2 = c2 – (b – x)2
a2 – x2 = c2 – (b2 – 2bx + x2)a2 – x2 = c2 – b2 + 2bx – x2
a2 – x2 + x2 = c2 – b2 + 2bx – x2 + x2
a2 = c2 – b2 + 2bx
(b-x)
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a2 = c2 – b2 + 2bx
a2 = c2 – b2 + 2b(a • CosC)
a2 = c2 – b2 + 2ab•CosCCos(m∡C) = x/a
a • Cos(m∡C) = x
a • CosC = x
1st
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a2 = c2 – b2 + 2bx
a2 = c2 – b2 + 2b(a • CosC)
a2 = c2 – b2 + 2ab•CosCCos(m∡C) = x/a
a • Cos(m∡C) = x
a • CosC = x
1st
2nd
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a2 = c2 – b2 + 2ab•CosC a2 – c2 = –b2 + 2ab•CosC
–c2 = –a2 – b2 + 2ab•CosC
c2 = a2 + b2 – 2ab•CosC
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c2 = a2 + b2 – 2ab•cosCClass Work:• Read MN;• Complete 5-96 f through 5-98.
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c2 = a2 + b2 – 2ab•CosC
x2 = 72 + 62 – 2 • 6 • 7 • Cos120°
x2 = 49 + 36 – 84 • Cos 120°
x2 = 85 – 84•(–0.5)
x2 = 85 + 42 = 127
x = √127 ≈ 11.27
c = x a = 7 b = 6 C = 120°
Class Work:• Read MN;• Complete 5-96 f through 5-98.
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Class Work:• Read MN;• Complete 5-96 f through 5-98.
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L-o-S L-o-Ctan-1
Class Work:• Read MN;• Complete 5-96 f through 5-98.
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L-o-S L-o-Ctan-1
x ≈ 4.9x ≈ 29.1° x ≈ 4.0
Class Work:• Read MN;• Complete 5-96 f through 5-98.