Question

which side is opposite to ∠r? triangle with vertices r, s, t, right-angled at s, sides: rs=7, st=24, rt=25 options: (red), (blue: st), (yellow), (green: all of the above)

Explanation:

Step1: Recall triangle side-angle opposite rule

In a triangle, the side opposite an angle is the side that does not form the angle. For \(\angle R\), the vertices of \(\angle R\) are \(R\), \(S\), and the other vertex connected to \(R\) is \(T\)? Wait, no, the triangle has vertices \(R\), \(S\), \(T\) with right angle at \(S\). So \(\angle R\) is at vertex \(R\), formed by sides \(RS\) and \(RT\)? Wait, no, in triangle \(RST\) with right angle at \(S\), the angles are at \(R\), \(S\), \(T\). The side opposite \(\angle R\) is the side that is not adjacent to \(\angle R\). Adjacent sides to \(\angle R\) are \(RS\) (length 7) and \(RT\)? Wait, no, the sides: \(RS = 7\) (from \(R\) to \(S\)), \(ST = 24\) (from \(S\) to \(T\)), \(RT = 25\) (from \(R\) to \(T\)). So \(\angle R\) is at \(R\), between \(RS\) and \(RT\)? Wait, no, the right angle is at \(S\), so the triangle is right-angled at \(S\), so sides: \(RS\) (leg), \(ST\) (leg), \(RT\) (hypotenuse). The angle at \(R\) (\(\angle R\)) is between \(RS\) and \(RT\), so the side opposite \(\angle R\) is the side that does not meet at \(R\), which is \(ST\).

Answer:

ST