Chapter 7.5, Problem 10PPS

To determine

To find: The distance between the bank and the intersection point.

Answer to Problem 10PPS

77 ft

Explanation of Solution

Given:

  

  $\Delta ABC\sim \Delta MNP$

  $AC=382$ ft

  $MP=248$ ft

Distance between gas station and junction = 50 ft

  $\Delta ABC\sim \Delta MNP$

Let the Gas station be at point $G$ .

Now, $GN$ will be the altitude.

Let the bank be at the point K.

Now, $BK$ will be the altitude.

In two similar triangles, the ratio of their corresponding sides, altitudes are equal.

  $\begin{array}{l}\frac{382}{248}=\frac{BK}{50}\\ \Rightarrow BK=77\end{array}$

Distance between bank and intersection is 77 ft.