anonymous
  • anonymous
Suppose a triangle has sides a, b, and c, and that a2 + b2 > c2. Let be the measure of the angle opposite the side of length c. Which of the following must be true? Check all that apply. The triangle is not a right triangle. The triangle is a right triangle. cos > 0 is an acute angle.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[a ^{2}+b ^{2}>c ^{2}\]
anonymous
  • anonymous
anonymous
  • anonymous
You could use the law of cosigns, however there are definitions that help answer this question. An acute triangle fits the definition of \( b^2 + c^2 > a^2\) where \(a\) is any side of the triangle. An obtuse triangle fits the definition of \(b^2 + c^2 < a^2\) where\( a\) is the side opposite of the obtuse angle. A triangle that is defined by the definition of \(a^2 + b^2 = c^2\) is a right triangle. (Pythagorean theorem.)

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