Question

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

Explanation:

Step1: Identify similar triangles

Triangles $\triangle PRE$ and $\triangle POC$ are similar (right triangles with shared $\angle OPC$).

Step2: Set up proportion

Corresponding sides are proportional:
$\frac{PR}{PO} = \frac{RE}{OC}$
Let $PR = x$. Then $PO = x + 125$. Substitute known values:
$\frac{x}{x + 125} = \frac{180}{350}$

Step3: Cross-multiply to solve for x

$350x = 180(x + 125)$
Expand right side:
$350x = 180x + 22500$
Subtract $180x$ from both sides:
$350x - 180x = 22500$
$170x = 22500$
Solve for $x$:
$x = \frac{22500}{170}$

Step4: Calculate and round

$x \approx 132.35$
Round to nearest foot: $x \approx 132$

Answer:

132 feet