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!!!Obtuse triangles:
Obtuse triangles are triangles in which one of their interior angles is more than 90 [{MathJax
fullWidth='false.'
\rm
^{\circ}
}] (obtuse angle) and the remaining two interior angles are each less than 90 [{MathJax
fullWidth='false.'
\rm
^{\circ}
}] ( acute angles). The three interior angles of a triangle must sum up to 180 [{MathJax
fullWidth='false.'
\rm
^{\circ}
}].
Let's use the cosine rule to determine the interior angles in the given triangle as follows:
[{MathJax fullWidth='false'
\rm
b=\sqrt {a^2 + c^2 - 2ac. cos B}\\
c\to \ side \ of \ triangle =9 \\
a\to \ side \ of \ triangle = 8 \\
b\to \ side \ of \ triangle = 16 \\
B\to \ interior \ angle \ opposite \ side \ b\\
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16=\sqrt {8^2 + 9^2 - 2(8 \times 9). cos B}\\
256= 64 + 81 - 144cosB\\
-144 Cos B = 256 - 64 -81 = 111\\
Cos \ B = \dfrac {111}{ -144} = -0.7708\\
B = cos^{-1} (-0.7708) = 140.43^{\circ}
B= 140.43^{\circ}
}]\\
[{MathJax fullWidth='false'
\rm
c=\sqrt {a^2 + b^2 - 2ab. cos C}\\
C\to \ interior \ angle \ opposite \ side \ c\\
9=\sqrt {8^2 + 16^2 - 2(16\times 8). cos C}\\
9=\sqrt {64 + 256 - 256. cos C}\\
81= 320- 256Cos C\\
256Cos C = 320 - 81\\
Cos \ C =\dfrac {239}{256} = 0.934\\
C = Cos^{-1} (0.934) = 20.1^{\circ}\\
A = 180 -( 21 + 140.43) = 18.57^{\circ}
}]
The given triangle has three interior angles with one angle formed between lines 9 and 8 is
more than 90[{MathJax fullWidth='false.'
\rm
^{\circ}
}],(140.43), which bears the name obtuse angle. The remaining angles are less than
90[{MathJax fullWidth='false.'
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\rm
^{\circ}
}] each, (18.57 and 21), and they are known as acute angles. Therefore, the obtuse triangle is
a triangle with one obtuse angle and two acute angles at the interior of the triangle, and the
sum of the three angles must add to 180 [{MathJax fullWidth='false.'
\rm
^{\circ}
}].
Thus, the given triangle is __[Obtuse triangle|]__

### Unformatted Attachment Preview

!!!Obtuse triangles: Obtuse triangles are triangles in which one of their interior angles is more than 90 [{MathJax fullWidth='false.' \rm ^{\circ} }] (obtuse angle) and the remaining two interior angles are each less than 90 [{MathJax fullWidth='false.' \rm ^{\circ} }] ( acute angles). The three interior angles of a triangle must sum up to 180 [{MathJax fullWidth='false.' \rm ^{\circ} }]. !!!Answer and Explanation: Let's use the cosine rule to determine the interior angles in the given triangle as follows: [{MathJax fullWidth='false' \rm b=\sqrt {a^2 + c^2 - 2ac. cos B}\\ c\to \ side \ of \ triangle =9 \\ a\to \ side \ of \ triangle = 8 \\ b\to \ side \ of \ triangle = 16 \\ B\to \ interior \ angle \ opposite \ side \ b\\ 16=\sqrt {8^2 + 9^2 - 2(8 \times 9). cos B}\\ 256= 64 + 81 - 144cosB\\ -144 Cos B = 256 - 64 -81 = 111\\ Cos \ B = \dfrac {111}{ -144} = -0.7708\\ B = cos^{-1} (-0.7708) = 140.43^{\circ} B= 140.43^{\circ} }]\\ [{MathJax fullWidth='false' \rm c=\sqrt {a^2 + b^2 - 2ab. cos C}\\ C\to \ interior \ angle \ opposite \ side \ c\\ 9=\sqrt {8^2 + 16^2 - 2(16\times 8). cos C}\\ 9=\sqrt {64 + 256 - 256. cos C}\\ 81= 320- 256Cos C\\ 256Cos C = 320 - 81\\ Cos \ C =\dfrac {239}{256} = 0.934\\ C = Cos^{-1} (0.934) = 20.1^{\circ}\\ A = 180 -( 21 + 140.43) = 18.57^{\circ} }] The given triangle has three interior angles with one angle formed between lines 9 and 8 is more than 90[{MathJax fullWidth='false.' \rm ^{\circ} }],(140.43), which bears the name obtuse angle. The remaining angles are less than 90[{MathJax fullWidth='false.' \rm ^{\circ} }] each, (18.57 and 21), and they are known as acute angles. Therefore, the obtuse triangle is a triangle with one obtuse angle and two acute angles at the interior of the triangle, and the sum of the three angles must add to 180 [{MathJax fullWidth='false.' \rm ^{\circ} }]. Thus, the given triangle is __[Obtuse triangle|]__ Name: Description: ...
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