Question

1. given the diagram below what is the length of (overline{rs}) or the distance across a body of water? 75 ft 106 ft 53 ft 87 m

Explanation:

Step1: Identify similar triangles

Triangles $\triangle RPS$ and $\triangle TQS$ are similar because $\angle RPS=\angle TQS = 90^{\circ}$ and the vertical - angles at point $S$ are equal.

Step2: Use the property of similar triangles

The ratios of corresponding sides of similar triangles are equal. Also, since the markings on the sides of the triangles indicate that the segments on $PQ$ are equal, we can assume that the two similar triangles are congruent (by Side - Angle - Side or other congruence criteria). So, $RS = ST$.

Step3: Determine the length of $RS$

Given that $ST = 53$ ft, then $RS=53$ ft.

Answer:

53 ft