Question

To indirectly measure the distance across a lake, Aubrey makes use of a couplelandmarks at points R and S. She measures QU, US, and TU as marked. Find thedistance across the lake (RS), rounding your answer to the nearest hundredth of ameter.

Answer 1

From the diagram given, we can see two similar triangles.

These are the smaller triangle QTU and the bigger triangle QRS.

Since the two triangles are similar, then the ratios of their sides must be equal, that is

`(QU)/(TU)=(QS)/(RS)`

Hence we have that

`\begin{gathered} (QU)/(TU)=(QS)/(RS) \\ (120)/(127.65)=(120+55)/(RS) \\ (120)/(127.65)=(175)/(RS) \\ RS=(127.65*175)/(120) \\ RS=186.15625 \end{gathered}`

Hence RS = 186.16m to the nearest hundredth.