6.20 the cosine law.notebook - nowyoudothemath.weebly.com...6.20 the cosine law.notebook 3 may 29,...
TRANSCRIPT
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6.20 The Cosine Law.notebook
1
May 29, 2020
Solutions
b2 = a2 + c2 2accos(B)
b2 = 122 + 102 2(12)(10)cos(72)
b2 = 169.835...
b = √(169.835...)
b = 13.03...
b = 13 cm
c2 = a2 + b2 2abcos(C)
c2 = 202 + 172 2(20)(17)cos(39)
c2 = 160.540...
c = √(160.540...)
c = 12.670...
c = 13 mm
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6.20 The Cosine Law.notebook
2
May 29, 2020
d2 = e2 + f2 2efcos(D)
d2 = 3.22 + 4.42 2(3.2)(4.4)cos(66)
d2 = 18.146...
d = √(18.146...)
d = 4.2598...
d = 4.3 m
z2 = x2 + y2 2xycos(Z)
z2 = 1.82 + 2.22 2(1.8)(2.2)cos(48)
z2 = 2.7804...
z = √(2.7804...)
z = 1.6675...
z = 1.7 cm
p2 = m2 + n2 2mncos(P)
p2 = 6.22 + 4.82 2(6.2)(4.8)cos(54)
p2 = 26.4950...
p = √(26.4950...)
p = 5.1473...
p = 5.1 mm
u2 = t2 + v2 2tvcos(U)
u2 = 1.82 + 1.42 2(1.8)(1.4)cos(52)
u2 = 2.0970...
u = √(2.0970...)
u = 1.4481...
u = 1.4 cm
d2 = e2 + f2 2efcos(D)
d2 = 1.12 + 1.62 2(1.1)(1.6)cos(74)
d2 = 2.7997...
d = √(2.7997...)
d = 1.6732...
d = 1.7 km
52Ο 74Ο
1.8 cm
1.4 cm 1.1 km
1.6 km
D
E
FTU
V
u d
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6.20 The Cosine Law.notebook
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May 29, 2020
r2 = p2 + q2 2pqcos(R)
r2 = 132 + 152 2(13)(15)cos(70)
r2 = 260.6121...
r = √(260.6121...)
r = 16.143
r = 16 cm
sin(P) p
= sin(R)r
sin(P) 13
= sin(70)16
sin(P) = 13sin(70)16sin(P) = 0.7635...
P = sin1(0.7635...)P = 49.7737...
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6.20 The Cosine Law.notebook
4
May 29, 2020
a2 = b2 + c2 2bccos(A)
a2 = 82 + 92 2(8)(9)cos(71)
a2 = 98.118...
a = √(98.118...)
a = 9.9055...
a = 10 m
sin(B) b
= sin(A)a sin(B) 8
= sin(71)10
sin(B) = 8sin(71)10sin(B) = 0.7564...
B = sin1(0.7564...)
B = 49.149...
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6.20 The Cosine Law.notebook
5
May 29, 2020
x2 = w2 + y2 2wycos(X)
x2 = 102 + 112 2(10)(11)cos(80)
x2 = 182.7974...
x = √(182.7974...)
x = 13.52...
x = 14 cm
sin(W) w
= sin(X)x sin(W) 10
= sin(80)14
sin(W) = 10sin(80)14sin(W) = 0.7034...
W = sin1(0.7034...)
W = 44.703...
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6.20 The Cosine Law.notebook
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May 29, 2020
b2 = h2 + s2 2hscos(B)
b2 = 2.02 + 2.52 2(2.0)(2.5)cos(70)
b2 = 6.8297...
b = √(6.8297...)
b = 2.6134...
b = 2.6 km
sin(H) h
= sin(B)b sin(H) 2.0
= sin(70)2.6
sin(H) = 2.0sin(70)2.6sin(H) = 0.7228...H = sin1(0.7228...)H = 46.289...
a)
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6.20 The Cosine Law.notebook
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May 29, 2020
a2 = b2 + c2 2bccos(A)
a2 = 9152 + 15252 2(915)(1525)cos(37)
a2 = 934059.950...
a = √(934059.950...)
a = 966.47...A
B
C
37Ο1525 m
915 m
a) b)
The runways are 966 metres apart
a
a2 = b2 + c2 2bccos(A)
a2 = 102 + 102 2(10)(10)cos(104.5)
a2 = 250.076...
a = √(250.076...)
a = 15.814...
a = 15.8 cm
104.5Ο 10 cm10 cm
A
BC
a)a
b) Both bond lengths are 10 cm which makes the triangle isosceles.