In a A B C , the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in AP , then the length of the third side can be

Step-by-step solution

Let A, B and C be the three angles of A B C and Let a=10 and b=9 It is given that the angles are in AP . 2 ~B = A + C on adding B both the sides, we get array l 3 ~B = A + B + C 3 ~B =180^ B =60^ array Now, we know B = a ²+ c ²- b ² 2 ac array l 60^ = 10²+ c ²-9² 2 10 c 1 2 = 100+ c ²-81 20 c c ²-10 c +19=0 c =5 6 array