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Manipal MET2013MathematicsSequences and Series

In a triangle, the length of the two larger sides are 24 and 22 , respectively. If the angles are in AP , then the third side is

Options

  1. A12+2 3
  2. B12-2 3
  3. C2 3 +2
  4. D2 3 -2

Correct answer

A. 12+2 3

Step-by-step solution

Since the angles are in A P , therefore 2 B=A+C 3 B=A+B+C 3 B=180^ B=60^ using the formula, A a = B b , we get A= a b B= 24 22 60^ = 6 3 11 Now; C= (180^ -(A+B) )= (A+B)= ( 6 3 11 ) ( 1 2 )+ 1- ( 6 3 11 )^2 ( 3 2 )= 1 22 ( 3 2 )(12+2 3 ) Now, c= b B C c=12+2 3 .

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