An emblem, as shown in the diagram above, considers a triangle \(ABC\) joined to the sector \(CBD\) of a circle with radius \(4cm\) and centre \(B \). The points \(A, B \) and \(D \) lie on a straight line with \(AB= 5cm\) and \(BD = 4cm\). Angle \(\angle BAC=0.6\) radians and \(AC \) is the longest side of the triangle \(ABC \).
(a) Show that angle \(\angle ABC=1.76\) radians, correct to \({3}\) significant figures. Were you able to show this?