Question

rectly measure the distance across a river, sebastian stands on one side
ark on the opposite bank. sebastian draws the diagram below to show the
r, the distance across the river. round your answer to the nearest foot.

agram is not to scale.)

Explanation:

Step1: Use similar triangles property

Since \(\triangle PRE\sim\triangle POC\) (by AA similarity, as \(\angle PRE=\angle POC = 90^{\circ}\) and \(\angle P\) is common), the ratios of corresponding sides are equal. So, \(\frac{PR}{PO}=\frac{RE}{OC}\).

Step2: Substitute the known values

We know \(PR = R\), \(PO=115\) ft, \(RE = 210\) ft, and \(OC = 275\) ft. Substituting into \(\frac{R}{115}=\frac{210}{275}\).

Step3: Solve for \(R\)

Cross - multiply: \(275R=115\times210\). Then \(R=\frac{115\times210}{275}\). Calculate \(115\times210 = 24150\), and \(R=\frac{24150}{275}\approx88\) ft.

Answer:

\(88\) ft