Question

To indirectly measure the distance across a lake, Isaac makes use of a couple landmarks at points G and H. He measures FJ, JH, and IJ as marked. Find the distance across the lake (GH), rounding your answer to the nearest hundredth of a meter.

Answer 1

To find:

The distance GH.

Solution:

In the given figure, in triangles GHF and IJF,

$\begin{gathered} \angle GFH=\angle IFJ(\text{ common angles}) \\ \angle FIJ=\angle FGH=90\text{ degrees \lparen given\rparen} \end{gathered}$

So, the triangles GHF and IJF are similar triangles by AA similarity criteria.

It is known that the ratio of corresponding sides of similar triangles are equal, So,

$\begin{gathered} \frac{FH}{FJ}=\frac{GH}{IJ} \\ \Rightarrow\frac{155+110}{155}=\frac{GH}{113.75} \\ \Rightarrow GH=\frac{265\times113.75}{155} \\ \Rightarrow GH=\frac{30143.75}{155} \\ \Rightarrow GH=194.48 \end{gathered}$

Thus, the answer is 194.48 meters.