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Question
In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:
the height of the tunnel
Solution
We have a cross section of a railway tunnel. `ΔOAB`is a right angled isosceles triangle, right angled at O. let OM be perpendicular to AB.
`OA=2 m`
Use Pythagoras theorem in `ΔOAB`to get,
`AB=(sqrt(2^2+2^2))m`
`= 2sqrt2 m`
Let the height of the tunnel be h. So,
`"Area of" ΔOAB=1/2(2)(2)`
`1/2(2sqrt2)(OM)=2`
Thus,
`OM=sqrt2m`
Therefore,
`h=(2+sqrt2)m`
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