The diagram shows the cross- section of a railway tunnel. If |AB| = 100m and the radius of the arc is 56m, calculate, correct to the nearest metre, the perimetre of the cross- section.
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.