The diagram shows the cross- section of a railway tunnel. If |AB| = 100m and

Explanation

From \(\Delta\) BCD,

\(\sin \theta = \frac{50}{56}\)

\(\theta = \sin^{-1} (0.8929)\)

\( < BCD = 63.23°\)

\(\therefore < ACB = 63.23° \times 2 = 126.46°\)

\(< ACB (reflex) = 360° - 126.46°\)

= \(233.54°\)

Perimeter of the arc = \(\frac{233.54}{360} \times 2 \times \frac{22}{7} \times 56\)

= \(228.35 m\)

Perimeter of the railway tunnel = Perimeter of the arc + |AB|

= 228.35 m + 100 m

= 328.35 m.