Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

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 )

Offline

**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

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

Offline

**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

1a2b3c2212 wrote:

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

I did translate the important parts of the text:

Kurre wrote:

Find

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

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Vi har

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

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

Offline

**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

JaneFairfax wrote:

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, ieOffline

Pages: **1**