Question

question
in \\( \triangle qrs, rs = 2, sq = 4 \\), and \\( qr = 3 \\). which list has the angles of \\( \triangle qrs \\) in order from largest to smallest?
answer
\\( m\angle r, m\angle q, m\angle s \\)
\\( m\angle s, m\angle r, m\angle q \\)
\\( m\angle q, m\angle s, m\angle r \\)
\\( m\angle q, m\angle r, m\angle s \\)
\\( m\angle r, m\angle s, m\angle q \\)
\\( m\angle s, m\angle q, m\angle r \\)

Explanation:

Step1: Apply the triangle - side - angle relationship

In a triangle, the larger side is opposite the larger angle.
In \(\triangle QRS\), we have \(SQ = 4\), \(QR=3\), and \(RS = 2\).

Step2: Determine the order of angles

Since \(SQ>QR>RS\), by the side - angle relationship (in a triangle, if \(a,b,c\) are the lengths of the sides of a triangle and \(A,B,C\) are the angles opposite to \(a,b,c\) respectively, \(a > b>c\) implies \(A > B > C\)).
The angle opposite \(SQ\) is \(\angle R\), the angle opposite \(QR\) is \(\angle S\), and the angle opposite \(RS\) is \(\angle Q\).

Answer:

\(m\angle R,m\angle S,m\angle Q\)