MHB A Guide to Growing Your Own Herbs""Growing Herbs: A Beginner's Guide

[Albert1]

View attachment 2748

 

[kaliprasad]

View attachment 2748

Spoiler

we have $\tan \alpha= \frac{1}{2} $
hence $\tan 2\alpha= \frac{2*\frac{1}{2}}{1-\frac{1}{4}}= \frac{4}{3} $

hence $DP = AD\tan\,2 \alpha =6$
so CP = 2

 

[chisigma]

View attachment 2748

[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{DP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$

 

[kaliprasad]

[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{CP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$

Spoiler

DP = 6 hence CP = 2

 

[Albert1]

thanks, kaliprasad and chisigma
you got it !
CP=2