Hampi, recognised by UNESCO as a World Heritage Site, preserves the magnificent ruins of the Vijayanagara Empire on the banks of the Tungabhadra river in Karnataka. A tourist sitting in a coracle at point \(A\) on the river observes the top \(C\) of a temple tower. The foot of the tower is at point \(B\), level with point \(A\).
The tourist imagines a right angled triangle \(ABC\), right angled at \(B\), where the horizontal distance \(AB =\) 40\(m\) and the height of the tower \(BC =\) 9 \(m.\)
(a) Find the value of \(\sin A\).
(b) Find the value of \(\sin C\).
(c) Find the value of \(\tan A + \cot C\).
(d) Find the value of \(\sec^2 A\).