6.30 Finding Angles Using the Cosine Law.notebook · PDF file 2020. 5. 30. · 6.30...
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6.30 Finding Angles Using the Cosine Law.notebook
1
May 30, 2020
Solutions
cos(A) = 2bc
b2 + c2 a2
cos(A) = 2(9)(10)
92 + 102 82
cos(A) = 180 117
cos(A) = 0.65
A = cos1(0.65) A = 49.458...
A = 49Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(B) = 2ac
a2 + c2 b2
cos(B) = 2(13)(10)
132 + 102 122
cos(B) = 260 125
cos(B) = 0.4807...
B = cos1(0.4807...) B = 61.264...
B = 61Ο
cos(C) = 2ab
a2 + b2 c2
cos(C) = 2(16)(17)
162 + 172 142
cos(C) = 544 349
cos(C) = 0.6415...
C = cos1(0.6415...) C = 50.092...
C = 50Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(K) = 2mn
m2 + n2 k2
cos(K) = 2(14)(16)
142 + 162 132
cos(K) = 448 283
cos(K) = 0.6316...
K = cos1(0.6316...) K = 50.824...
K = 51Ο
cos(U) = 2tv
t2 + v2 u2
cos(U) = 2(1.8)(2.5)
1.82 + 2.52 2.42
cos(U) = 9
3.73
cos(U) = 0.4144...
U = cos1(0.4144...) U = 65.515...
U = 66Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(G) = 2fh
f2 + h2 g2
cos(G) = 2(5.1)(6.2)
5.12 + 6.22 4.82
cos(G) = 63.24 41.41
cos(G) = 0.6548...
G = cos1(0.6548...) G = 49.094...
G = 49Ο
A
RD
H
WN
190 mm
170 mm
210 mm
1.4 km
1.7 km 1.2 km
cos(D) = 2ar
a2 + r2 d2
cos(D) = 2(170)(190)
1702 + 1902 2102
cos(D) = 64600 20900
cos(D) = 0.3235...
D = cos1(0.3235...) D = 71.123... D = 71Ο
cos(W) = 2hn h2 + n2 w2
cos(W) = 2(1.4)(1.2)
1.42 + 1.22 1.72
cos(W) = 3.36 0.51
cos(W) = 0.1517...
W = cos1(0.1517...) W = 81.269... W = 81Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(J) = 2mv
m2 + v2 j2
cos(J) = 2(8.3)(12.0)
8.32 + 12.02 10.02
cos(J) = 199.2 112.89
cos(J) = 0.5667...
J = cos1(0.5667...) J = 55.478...
J = 55.5Ο
cos(V) = 2jm
j2 + m2 v2
cos(V) = 2(10.0)(8.3)
10.02 + 8.32 12.02
cos(V) = 166 24.89
cos(V) = 0.1499...
V = cos1(0.1499...) V = 81.376...
cos(M) = 2jv
j2 + v2 m2
cos(M) = 2(10.0)(12.0)
10.02 + 12.02 8.32
cos(M) = 240 175.11
cos(M) = 0.7296...
M = cos1(0.7296...) M = 43.145...
V = 81.4Ο M = 43.1Ο
cos(J) = 2mv
m2 + v2 j2
cos(J) = 2(8.3)(12.0)
8.32 + 12.02 10.02
cos(J) = 199.2 112.89
cos(J) = 0.5667...
J = cos1(0.5667...) J = 55.478...
J = 55.5Ο
b) sin(V) v = sin(J) j
sin(V) 12.0 =
sin(55.5) 10.0
sin(V) = 12.0sin(55.5)10.0 sin(V) = 0.9889...
V = sin1(0.9889...)
V = 81.475...
V = 81.5Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(T) = 2uv
u2 + v2 t2
cos(T) = 2(5)(7)
52 + 72 62
cos(T) = 70 38
cos(T) = 0.5428...
T = cos1(0.5428...) T = 57.121...
T = 57.1Ο
sin(V) v =
sin(T) t
sin(V) 7 =
sin(57.1) 6
sin(V) = 7sin(57.1)
6 sin(V) = 0.9795...
V = sin1(0.9795...)
V = 78.394...
V = 78.4Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(B) = 2gn
g2 + n2 b2
cos(B) = 2(12)(15)
122 + 152 142
cos(B) = 360 173
cos(B) = 0.4805...
B = cos1(0.4805...) B = 61.278...
B = 61.3Ο
sin(G) g =
sin(B) b
sin(G) 12 =
sin(61.3) 14
sin(G) = 12sin(61.3)14 sin(G) = 0.7518...
G = sin1(0.7518...)
G = 48.749...
G = 48.7Ο
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(A) = 2bc
b2 + c2 a2
cos(A) = 2(3.8)(3.8)
3.82 + 3.82 4.82
cos(A) = 28.88 5.84
cos(A) = 0.2022...
A = cos1(0.2022...) A = 78.333...
A = 78Ο
B = 51Ο C = 51Ο
AB
C
The triangle is isosceles where
6.30 Finding Angles Using the Cosine Law.notebook
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May 30, 2020
cos(B) = 2ac
a2 + c2 b2
cos(B) = 2(5.0)(4.1)
5.02 + 4.12 6.02
cos(B) = 41.0 5.81
cos(B) = 0.1417...
B = cos1(0.1417...) B = 81.853...
B = 82Ο
sin(C) c =
sin(B) b
sin(C) 4.1 =
sin(82) 6.0
sin(C) = 4.1sin(82)6.0 sin(C) = 0.6766...
C = sin1(0.6766...)
C = 42.584...
C = 43Ο
