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Manipal MET2014MathematicsTrigonometric Ratios & Identities

If ^2 A+ ^2 C= ^2 B , then A B C is

Options

  1. Aequilateral
  2. Bright angled
  3. Cisosceles
  4. DNone of the above

Correct answer

B. right angled

Step-by-step solution

Given, ^2 A+ ^2 C= ^2 B Obviously it is not an equilateral triangle because A=B=C=60^ does not satisfy the given condition. But B=90^ , then ^2 B=1 and aligned ^2 A+ ^2 C= & ^2 A+ ^2 ( 2 -A ) = & ^2 A+ ^2 A=1 aligned Hence, this satisfies the condition, so it is a right angled triangle but not necessarily isosceles triangle.

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