Question

to indirectly measure the distance across a river, jonathan stands on one side of the river and uses sight-lines to a landmark on the opposite bank. jonathan draws the diagram below to show the lengths and angles that he measured. find pr, the distance across the river. round your answer to the nearest foot. (diagram is not to scale.) answer attempt 1 out of 2

Explanation:

Step1: 确定相似三角形

图中\(\triangle PRE\)和\(\triangle POC\)都是直角三角形，且\(\angle P\)为公共角，所以\(\triangle PRE \sim \triangle POC\)（AA相似）。

Step2: 利用相似三角形性质列比例

相似三角形对应边成比例，即\(\frac{PR}{PO}=\frac{RE}{OC}\)。已知\(PO = PR + 115\)，\(RE = 255\)，\(OC = 320\)，代入得\(\frac{PR}{PR + 115}=\frac{255}{320}\)。

Step3: 解方程求PR

交叉相乘：\(320PR = 255(PR + 115)\)，展开得\(320PR = 255PR + 255\times115\)，移项得\(320PR - 255PR = 29325\)，即\(65PR = 29325\)，解得\(PR=\frac{29325}{65}=451.15\approx451\)（英尺）。

Answer:

\(451\)英尺