Question

Engineers and surveyors often determine distances that cannot be measureddirectly by using similar triangles like the ones shown below.30River42 ft80 ftUsing the information from the drawing, which of these is closest to the distancefrom Point Aon one bank to Point Eon the opposite bank?

Answer 1

Answer:

102 feet

Explanation:

First, find the length of AB:

In the larger triangle ADC:

$\begin{gathered} \sin 30=\frac{80}{AB+42} \\ 0.5=\frac{80}{AB+42} \\ 0.5(AB+42)=80 \\ AB+42=\frac{80}{0.5} \\ AB=160-42 \\ AB=118 \end{gathered}$

Since we already know the length of AB:

$\begin{gathered} \cos 30=\frac{AE}{AB} \\ \cos 30=\frac{AE}{118} \\ AE=118\times\cos 30 \\ AE=102.19 \\ AE\approx102\text{ f}eet \end{gathered}$

The distance from Point A on one bank to Point E on the opposite bank is closest to 102 feet.