Question

given the diagram below what is the length of rs or the distance across a body of water?
45 m
85 m
60 m
75 m

Explanation:

Step1: Prove the congruence of triangles

Since \( \angle RPS=\angle TQS = 90^{\circ}\), \(PS = QS\) (marked as equal), and \( \angle RSP=\angle TSQ\) (vertically - opposite angles), by the ASA (Angle - Side - Angle) congruence criterion, \(\triangle RPS\cong\triangle TQS\).

Step2: Use the property of congruent triangles

For congruent triangles \(\triangle RPS\) and \(\triangle TQS\), the corresponding sides are equal. So \(RS = TS\). Given \(TS = 85m\), then \(RS=85m\).

Answer:

\(85m\) (the second option)