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KCET2010MathematicsProperties of Triangles

This sides of a triangle are 6+2 3 , 4 3 and 24 . The tangent of the smallest angle of the triangle is

Options

  1. A1 3
  2. B2 -1
  3. C3
  4. D1

Correct answer

A. 1 3

Step-by-step solution

Given that, side of triangles are a =6+2 3 , ~b =4 3 and c = 24 Here, we observe that the side ' c ' is small, hence the angle C is also small. Then, aligned & C= a²+b²-c² 2 a b =& (6+2 3 )²+(4 3 )²-( 24 )² 2(6+2 3 )(4 3 ) aligned aligned & C= 36+12+48-24+24 3 16 3 (3+ 3 ) & C= 72+24 3 16 3 (3+ 3 ) = 24(3+ 3 ) 16 3 (3+ 3 ) & C= 3 2 3 = 3 2 & C= 30^ C=30^ & The smallest angle C=30^ & Hence, the tangent of smallest angle is & tan C= 30^ &= 1 3 aligned

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