Math Is Fun Forum

Kurre

Member

Registered: 2006-07-18

Posts: 280

Geometry problem, nice solution

http://g.imagehost.org/0615/3462.jpg
Find

This is an easy problem if you use the standard approach with trigonometry (the problem is for ~17 years old students). But I found a much nicer geometrical method, without using any trigonometry.
So my challenge for you is to find it.
(or solve it any other way without trigonometry is fine too )

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Geometry problem, nice solution

HOW TO READ THAT LANGUAGE??? can translate into english pls? thx

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Geometry problem, nice solution

HOW TO READ THAT LANGUAGE??? can translate into english pls? thx

I did translate the important parts of the text:

Find

Altough I should maybe have written that the figure consists of three squares, but that is kind of obvious.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Geometry problem, nice solution

Vi har

och

. Om

så

.

.

Det är ett skönt problem. Tack så mycket, Kurre.

Last edited by JaneFairfax (2009-08-19 06:58:40)

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Geometry problem, nice solution

http://g.imagehost.org/0615/3462.jpg

Vi har

och

. Om

så

.

.

Det är ett skönt problem. Tack så mycket, Kurre.

Yes that is the trigonometric approach
Good job!

Have you been studying swedish? I think I remember that you wrote that you are interested in languages. Nicely done!

Anyway here is my method:

Reflect AB in the horizontal line and draw line BC as in 2. Now reflect the triangle ABC in AC to make a quadrilateral as in 3. Now, all angles in the quadrilateral ABCD are equal, and all sides are equal, thus it is a square, and since AC is a diagonal,

must be half of a right angle, ie