Question

To indirectly measure the distance across a lake, Jeremiah makes use of a couplelandmarks at points O and P. He measures NR, RP, and Q R as marked. Find thedistance across the lake (OP), rounding your answer to the nearest hundredth of ameter.

Answer 1

Notice that triangles NPQ and NRQ are similar, then:

`(OP)/(QR)=(NP)/(NR).`

Now, notice that:

`PN=NR+RP.`

Therefore:

`(OP)/(QR)=(NR+RP)/(NR).`

Multiplying the above result by QR we get:

`\begin{gathered} (OP)/(QR)* QR=(NR+RP)/(NR)* QR, \\ OP=(NR+RP)/(NR)* QR. \end{gathered}`

Substituting NR=125m, RP=65m, and QR=106.75m we get:

`OP=(125m+65m)/(125m)*106.75m.`

Simplifying the above result we get:

`\begin{gathered} OP=(190m)/(125m)*106.75m \\ =162.26m. \end{gathered}`

Answer:

`OP=162.26m.`