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July 12th, 2018, 09:25 AM   #1
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Thumbs up Urgent help needed!

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

Last edited by skipjack; July 12th, 2018 at 01:20 PM. Reason: Forgot to add a URL
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July 12th, 2018, 10:01 AM   #2
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That link doesn't work for me...try attaching the image perhaps.
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July 12th, 2018, 10:48 AM   #3
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Here's the image:
Attached Images
File Type: jpg 29bhop1.jpg (67.3 KB, 7 views)

Last edited by greg1313; July 12th, 2018 at 01:41 PM.
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July 12th, 2018, 12:03 PM   #4
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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
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July 12th, 2018, 12:08 PM   #5
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Construct a perpendicular from where $r$ meets $s$ to $r$ on the opposite side and use the Pythagorean theorem.
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July 12th, 2018, 12:11 PM   #6
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What happened to the OP?
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July 12th, 2018, 12:57 PM   #7
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Quote:
Originally Posted by MarkFL View Post
What happened to the OP?
eaten... by snakes
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