This is the basic and exam oriented question from trigonometric ratios in which we have given a figure of right angled triangle ABC in which ∠B = 90° and ∠A = 30°. If BC = 6 cm, We have to calculate (i) AB, (ii) AC.
RS Aggarwal, class 10, chapter 11, question no 21
Draw a right angled △ABC using given instructions:
Here sin30=BC/AC
1/2=6/AC
Or AC=12 cm
By Pythagoras theorem:
(AB)^2=(AC)^2−(BC)^2
=(12)^2−(6)^2
=108
AB=6√3cm.