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

Home > Shapes > Geometry
Angle ABC (Posted on 2006-02-25) Difficulty: 3 of 5
In a triangle ABC, D is the midpoint of BC. Join AD. Angle ADB = 45 degree and angle ACB = 30 degree. Find angle ABC.

No Solution Yet Submitted by akash    
Rating: 2.3000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: An algebraic solution | Comment 7 of 13 |
(In reply to An algebraic solution by Eric)

I don't see how it is possible to let AD = DB = 1.  According to the problem statement, D is the midpoint of BC, so it is CD that equals DB.  What one needs to prove is that AB=BD×sqrt(2).  This can be done by calling B the origin, writing equations for the lines AC and AD, and solving for the coordinates of A.  This does work out and proves that ABC is similar to BDA so that angle ABC is 105 degrees just as I predicted in my earlier comment.

  Posted by Richard on 2006-02-26 04:56:02

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

Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information