Question

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.

Answer 1

\[a ^{2}+b ^{2}>c ^{2}\]

Answer 2

@welshfella

Answer 3

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.)