A triangle has angles in ratio 2:3:5.

(a(i)) Show it is right-angled. [1]

(a(ii)) The hypotenuse is 12 cm. Use trigonometry to find its shortest side. [3]

Another right triangle has sides in ratio 3:4:5.

(b(i)) Its shortest side is 7.8 cm. Find the longest side. [2]

(b(ii)) Find its smallest angle. [3]