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AP EAMCET201726 Apr 2017Morning ShiftMathematicsProperties of TrianglesActual

In A B C , if b =c-a , (where is an acute angle), then (c-a) =

Options

  1. A2 c a B 2
  2. B2 c a B 2
  3. C2 c a B 2
  4. D2 c a B 2

Correct answer

B. 2 c a B 2

Step-by-step solution

We have, b =c-a = c-a b aligned & = b^2-(c-a)^2 b & and = b^2-(c-a)^2 (c-a) aligned and = b^2-(c-a)^2 (c-a) Now, (c-a) = b^2-(c-a)^2 aligned & = b^2-c^2-a^2+2 a c = - (c^2+a^2-b^2 )+2 a c & = 2 a c-2 a c B [ Using cosine rule] & = 2 a c 1- B & = 2 a c 2 ^2 B 2 =2 a c B 2 aligned

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