Question

To directly measure the distance across a river, Makayla stands on one side of the diagram below to show the lengths and angles that she measures. Find PR, the distance across the river. Round your answer to the nearest foot.

Answer 1

287 ft

Explanation:

Side lengths of similar triangles are proportional, so we can write and solve a proportion that will tell the length of PR.

ΔRPE ~ ΔOPC so ratios of corresponding sides are the same:

PR/PO = RE/OC

PR/(PR +165) = 235/370 . . . . . substitute known values

74·PR = 47·(PR +165) . . . . . . . . multiply by 74(PR +165)

27·PR = 7755 . . . . . . . . . . simplify, subtract 47·PR

PR = 287 2/9 . . . . . . . divide by 27

The distance across the river is about 287 feet.