A, B and C name three towns. The bearing of B from A is 110^{\circ}. The bearing of C from B is 280^{\circ}. AC = 38 km and AB = 50 km.
(a(i))[2]
Find the bearing from B to A.
(a(ii))[5]
Calculate $\angle BAC$.
(a(iii))[3]
A new road is constructed from A to meet the straight road BC. Calculate the minimum possible length of this road.
(b(i))[1]
Show that the equation $x^2 - 25x - 2200 = 0$ is obtained.
(b(ii))[4]
Solve $x^2 - 25x - 2200 = 0$. Give full working, and state your answers correct to 2 decimal places.
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