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