Answer:
[tex]Distance=6.03504\ km[/tex]
Step-by-step explanation:
Let the places are denoted by following symbols:
[tex]Main\ Gate=G\\Bird\ Sanctuary=B\\Train\ Depot= T\\Mantee\ Spring=M\\Elephant\ House=E[/tex]
In the [tex]\triangle TEM[/tex] and [tex]\triangle TBG[/tex]
[tex]\angle E=\angle B\\\angle M=\angle G\\\angle MTE=\angle TBG[/tex]
By [tex]AAA[/tex] [tex]\triangle TEM[/tex] and [tex]\triangle TBG[/tex] are similar.
[tex]\frac{TG}{TM}=\frac{TB}{TE}\\\\TG=TM\times \frac{TB}{TE}\\\\=4200\times \frac{2000}{3500}\\\\=4200\times \frac{4}{7}\\\\=2400\\\\\\MG=MT+TG\\\\MG=4200+2400\\\\MG=6600\ yards\\\\MG=6600\times 0.000914\ km\\\\MG=6.03504\ km[/tex]
