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 Seeking The Angle (Posted on 2007-10-29)
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 | 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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