Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 16 cm².

A river has parallel banks that run directly east-west. From the southern bank, John takes a bearing to a particular point on the opposite bank, and the bearing is \(043^\circ\text{T}\).   He then walks 12 m due east and takes a second bearing to the point, and this is \(306^\circ\text{T}\).   Find the width of the river, correcting to one decimal place.

Find \(x\), correcting to one decimal place.

Convert \(112.4^\circ \) to radians, correct to 3 significant figures.

Find \(\theta \), if \(\sin \theta = 0.6\) and \(\cos \theta = 0.8\), correct to 2 decimal places.

If  \(\tan x = – \dfrac{4}{3}\)  and  \(\dfrac{\pi }{2} < x < \pi \),   \(\sin x = \dfrac{a}{5}\)  and  \(\cos x = \dfrac{b}{5}\).   Find \(a\) and \(b\).

Find the angle of inclination, in radian correcting to two significant figures, of a line having a gradient of 3.2.

Find  \(A\),  if  \({\cos ^3}\theta + \cos \theta {\sin ^2}\theta = A\cos \theta \).

Solve  \(\sin \left( {4x – 180^\circ } \right) = 0\)  for  \( 0^\circ \le x \le 180^\circ \).   Write five answers in ascending order.

Solve  \(\tan \left( {4x – 180^\circ } \right) = 0\)  for  \(0^\circ \le x \le 180^\circ \).   Write five answers in ascending order, , correcting to one decimal place where necessary.