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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.

Respuesta :

nobillionaireNobley
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:

[tex] \frac{x}{60} = \frac{x+45}{90} \\ \\ \Rightarrow90x=60x+2700 \\ \\ \Rightarrow30x=2700 \\ \\ \Rightarrow x=90m[/tex]

Therefore, the distance across the river is 90m.