Question

In the diagram, triangle ABC is right-angled and D is the mid-point of BC. Angle DAC=30 degrees and angle BAD =x degrees, denoting the length of AD by l,

(i) express each of AC and BC in terms of l, and show that AB= (1/2)l sqrt 7

(ii) show that x=tan^-1 (2 over sqrt 3) -30.