Question

to measure the distance across a river, henry stands on one side of the river an to a landmark on the opposite bank. find the distance across the river. round y nearest foot.

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 ratio of corresponding sides is equal. Let \(PR = 150\) ft, \(RE=205\) ft, \(OC = 275\) ft and \(PO=x\) (distance across the river). Then \(\frac{PR}{PO}=\frac{RE}{OC}\).

Step2: Substitute values and solve for \(x\)

Substitute the values into the proportion \(\frac{150}{x}=\frac{205}{275}\). Cross - multiply: \(205x=150\times275\). So \(x=\frac{150\times275}{205}\). Calculate \(150\times275 = 41250\), then \(x=\frac{41250}{205}\approx201\) ft.

Answer:

\(201\) ft