This is the basic and conceptual question from trigonometric ratios in which we have given a figure of right angled triangle ABC right angled at B and we have to find the length and BC and AB if ∠A = 45° and AC = 3√2 cm.
RS Aggarwal, Class 10, chapter 11, question no 22.
From right angled △ABC,
(i) BC/AC=sin45∘
BC/3√2=1/√2
Or BC=3
(ii) By Pythagoras theorem
(AB)^2=(AC)^2−(BC)^2
=(3√2)^2−(3)^2
=18−9
=9
AB=3 cm.