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MHT CET202012 Oct 2020Morning ShiftMathematicsProperties of TrianglesActual

If two angles of ABC are 4 and 3 , then the ratio of the smallest and greatest side is

Options

  1. A3 : 2
  2. B( 3 -1): 1
  3. C( 3 +1):( 3 -1)
  4. D( 3 +1): 1

Correct answer

B. ( 3 -1): 1

Step-by-step solution

Two angles of triangle are 4 and 3 Let the third angle be . array l 4 + 3 + = 45^ +60^ + =180^ =75^ array We know that side opposite to smallest angle is the smallest side and side opposite to largest angle is the largest side. c 75^ = a 45^ We know that 75^ = 3 +1 2 2 c (2 2 ) 3 +1 = a 2 a c = 2 3 +1 By rationalizing, we get a c = 3 -1 1 Note : 75^ can be calculated as follows : aligned 75^ &= (45^ +30^ ) &= ( 1 2 3 2 )+ ( 1 2 1 2 )= 3 +1 2 2 aligned

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