Question

to indirectly measure the distance across a river, isaac stands on one side of the river and uses sight - lines to a landmark on the opposite bank. isaac 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: Identify similar triangles

Triangles $PR E$ and $POC$ are similar because $\angle PRE=\angle POC = 90^{\circ}$ and $\angle RPE=\angle OPC$ (common - angle).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{PR}{PO}=\frac{RE}{OC}$.
We know that $PO = PR + 105$, $RE = 130$ ft, and $OC = 245$ ft. Let $PR=x$. Then the proportion becomes $\frac{x}{x + 105}=\frac{130}{245}$.

Step3: Cross - multiply

Cross - multiplying gives us $245x=130(x + 105)$.
Expand the right - hand side: $245x=130x+130\times105$.
$245x=130x + 13650$.

Step4: Solve for $x$ (which is $PR$)

Subtract $130x$ from both sides: $245x-130x=13650$.
$115x=13650$.
Divide both sides by 115: $x=\frac{13650}{115}=118.695652$.

Step5: Round to the nearest foot

Rounding $118.695652$ to the nearest foot gives $119$ ft.

Answer:

$119$ ft