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Seeking The Angle (Posted on 2007-10-29) Difficulty: 2 of 5
A point S is taken on the side QR of triangle PQR such that RS = 2SQ. It is known that Angle PQR = 45o and Angle SPQ = 15o

Determine Angle PRQ.

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution Solution | Comment 2 of 4 |

     |QS|        |QS|         |PS|         |PS|
  --------- = ---------- = ---------- = ---------
   sin(15)     sin(QPS)     sin(PQS)     sin(45)
      2|QS|         |RS|         |PS|        |PS|
  ------------ = ---------- = ---------- = --------
   sin(120-x)     sin(RPS)     sin(PRS)     sin(x)
  2*sqrt(2)*sin(15)sin(x) = sin(120-x)          (1)
                = sin(120)*cos(x) - cos(120)*sin(x)
                = [sqrt(3)*cos(x) + sin(x)]/2
                    sqrt(3)
  tan(x) = -----------------------
            4*sqrt(2)*sin(15) - 1
         ~= 75 degrees
  Plugging x = 75 into equation (1), we see that
  angle PRQ is exactly 75 degrees.
 

  Posted by Bractals on 2007-10-29 12:04:57
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