(a) Given that \(\sin x = \frac{5}{13}, 0° < x < 90°\), find \(\frac{\cos x - 2\sin x}{2\tan x}\). (b) A ladder, LA, leans against a vertical pole at a poin...

(a) Given that \(\sin x = \frac{5}{13}, 0° < x < 90°\), find \(\frac{\cos x - 2\sin x}{2\tan x}\).

(b) A ladder, LA, leans against a vertical pole at a point L which is 9.6metres above the groung. Another ladder, LB, 12 metres long, leans on the opposite side of the pole and at the same point L. If A and B are 10 metres apart and on the same straight line as the foot of the pole, calculate, correct to 2 significant figures, the :

(i) length of ladder LA  (ii) angle which LA makes with the ground.