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

194.48

Explanation:

Answer 2

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} (FH)/(FJ)=(GH)/(IJ) \\ \Rightarrow(155+110)/(155)=(GH)/(113.75) \\ \Rightarrow GH=(265*113.75)/(155) \\ \Rightarrow GH=(30143.75)/(155) \\ \Rightarrow GH=194.48 \end{gathered}`

Thus, the answer is 194.48 meters.