Question

Calculate the distance across this river,

PR, by sighting a pole, at point P, on
the opposite bank. Points R and O
are collinear with point P. Point C is
chosen so that OC PO. Lastly,
point E is chosen so that P, E, and C
are collinear and RE PO. Also
explain why PRE POC.

Answer 1

Since ΔPRE is similar to POC, then the ratio of the corresponding sides are equal.

Let the distance across the river be x and given that RO is 45m, OC is 90m and RE is 60m, then:


`(x)/(60) = (x+45)/(90) \\ \\ \Rightarrow90x=60x+2700 \\ \\ \Rightarrow30x=2700 \\ \\ \Rightarrow x=90m`

Therefore, the distance across the river is 90m.