Maths-
SAT
Easy

Question

In a right triangle, the tangent of one of the two acute angles is fraction numerator square root of 3 over denominator 3 end fraction . What is the tangent of the other acute angle?

  1. negative fraction numerator square root of 3 over denominator 3 end fraction 
  2. negative fraction numerator 3 over denominator square root of 3 end fraction 
  3. fraction numerator square root of 3 over denominator 3 end fraction 
  4. fraction numerator 3 over denominator square root of 3 end fraction 

The correct answer is: fraction numerator 3 over denominator square root of 3 end fraction


    Let θ be an acute angle
    rightwards double arrow tan theta equals fraction numerator square root of 3 over denominator 3 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    The other acute angle is 90 – θ
    rightwards double arrow Tan left parenthesis 90 minus theta right parenthesis equals cot theta equals fraction numerator 1 over denominator Tan theta end fraction equals fraction numerator 1 over denominator fraction numerator 1 over denominator square root of 3 end fraction end fraction equals fraction numerator 3 over denominator square root of 3 end fraction equals square root of 3

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