Answer: The answer is (C) [tex]\sqrt3:2.[/tex]
Step-by-step explanation: As given in the question, a right-angled triangle ABC is drawn in the attached figure, where
∠A = 30°, ∠B = 90° and ∠C = 60°.
The longest leg is AB, AC is the hypotenuse and BC is the shortest leg.
To find :- AB : AC.
We have from the right-angled triangle ABC,
[tex]\dfrac{AB}{AC}=\dfrac{p}{h}=\sin 60^\circ\\\\\Rightarrow AB:AC=\dfrac{\sqrt3}{2}\\\\\Rightarrow AB:AC=\sqrt3:2.[/tex]
Thus, the correct option is (C).
