All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Take Unit Length, Get PR (Posted on 2007-06-17) Difficulty: 3 of 5
The perpendicular from vertex P of the triangle PQR meets QR at the point S. A point T is located on PR such that QT=TR=RS=1.

What is the length of PR, given that Angle QPR=90o?

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution (other way) Comment 2 of 2 |
Consider triangle QTR, QT=TR=1 which implies that 
<TQR=<TRQ (let it be a) =a.
<PQR=90-<PRQ = 90-a
Therefore <PQT=90-a-a=(90-2a)
Consider triangle PTQ, apply sine rule
QT/sin90 = PT/sin(90-2a)
Consider triangle PRS, <SPR=90-<PRS=90-a
So, PR sin(90-a)=SR
=> PRcosa=1, so, sub. cos(a)=1/PR in eq(1)
PR^3=2 => PR = 2^(1/3) (or) cube-root(2)

Edited on August 7, 2007, 7:05 am
  Posted by Praneeth Yalavarthi on 2007-07-10 07:13:14

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information