The angles A , B & C of a ∆ A B C are in A . P . and a : b = 1 : 3 . If c = 4 c m , then the area (in s q . c m ) of this triangle is:

Step-by-step solution

In ∆   A B C , angles A ,   B ,   C are in A . P . hence 2 ∠ B = ∠ A + ∠ C Also, by angle sum property ∠ A + ∠ B + ∠ C = 180 ° ⇒ 2 ∠ B + ∠ B = 180 ° ⇒ ∠ B = 60 ° . Now a : b = 1 : 3 By, using sine rule, we have sin A a = sin B b = sin C c ⇒ sin A a = sin B b ⇒ sin A sin 60 ° = a b ⇒ sin A = 1 3   · 3   2 = 1 2 ⇒ ∠ A = 30 ° and hence ∠ C = 90 ° Thus,