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

 

Answer 1

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`