Question

How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from

yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.

Answer 1

`Distance=6.03504\ km`

Explanation:

Let the places are denoted by following symbols:

`Main\ Gate=G\\Bird\ Sanctuary=B\\Train\ Depot= T\\Mantee\ Spring=M\\Elephant\ House=E`

In the
`\triangle TEM` and
`\triangle TBG`

`\angle E=\angle B\\\angle M=\angle G\\\angle MTE=\angle TBG`

By
`AAA`
`\triangle TEM` and
`\triangle TBG` are similar.

`(TG)/(TM)=(TB)/(TE)\\\\TG=TM* (TB)/(TE)\\\\=4200* (2000)/(3500)\\\\=4200* (4)/(7)\\\\=2400\\\\\\MG=MT+TG\\\\MG=4200+2400\\\\MG=6600\ yards\\\\MG=6600* 0.000914\ km\\\\MG=6.03504\ km`