ArusaWaseem1784

Hi guys, I was just wondering how I should proceed to answer this question. I've tried the double-angle cosine formula (advised to try by a friend), but still can't figure out the answer. Any help would be much appreciated!

http://tinypic.com/r/29bhop1/9

MarkFL

That link doesn't work for me...try attaching the image perhaps.

greg1313

Here's the image:

Attached Images

29bhop1.jpg (67.3 KB, 7 views)

romsek

Well you've got an isosceles triangle with a angle of $\dfrac \pi 4$ between the two equal sides.

because $\dfrac \pi 4 = \dfrac {2\pi}{8}$

so

$\dfrac s 2 = r \sin\left(\dfrac 1 2 \dfrac \pi 4\right)$

$s = 2 r \sin\left(\dfrac \pi 8\right)$

$s^2 = 4r^2 \sin^2\left(\dfrac \pi 8\right)$

$s^2 = 4r^2 \cdot \dfrac{1}{4} \left(2-\sqrt{2}\right)$

$s^2 = r^2 \left(2-\sqrt{2}\right)$

of course the magic here is

$\sin^2\left(\dfrac \pi 8\right) = \dfrac{1}{4} \left(2-\sqrt{2}\right)$

I leave that to you to show

greg1313

Construct a perpendicular from where $r$ meets $s$ to $r$ on the opposite side and use the Pythagorean theorem.

MarkFL

What happened to the OP?

romsek

eaten... by snakes