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AP EAMCET20224 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual

If in a triangle ABC , a = 2 , b = 3 and c = 4 , then tan A 2 =

Options

  1. A3 15
  2. B4 15
  3. C2 15
  4. D1 15

Correct answer

D. 1 15

Step-by-step solution

Given, In a triangle ABC , a = 2 ,   b = 3 and c = 4 , Now we know that tan A 2 = s - b s - c s s - a where s = a + b + c 2 Now using the above formula we will find the required value, So, s = 2 + 3 + 4 2 = 4 . 5 Now tan A 2 = 4 . 5 - 3 4 . 5 - 4 4 . 5 4 . 5 - 2 ⇒ tan A 2 = 1 . 5 × 0 . 5 4 . 5 × 2 . 5 ⇒ tan A 2 = 15 × 5 45 × 25 ⇒ tan A 2 = 1 15

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