Question-80237

Question Number 80237 by M±th+et£s last updated on 01/Feb/20

Commented by M±th+et£s last updated on 01/Feb/20

i f A B C D E F G i s a h e p t a g o n a n d A B = 1

H I J K L M i s h e x a g o n

t h a n f i n d H I

Commented by mr W last updated on 01/Feb/20

H I J K L M N i s a l s o a h e p t a g o n!

Commented by M±th+et£s last updated on 01/Feb/20

y o u a r e r i g h t s i r i t s t y p o

Commented by Tony Lin last updated on 01/Feb/20

l e t I E = x

\frac{x^{2} + x^{2} - 1^{2}}{2 x^{2}} = c o s \frac{5 π}{7}

l e t 2 x^{2} = t

\Rightarrow \frac{t - 1}{t} = c o s \frac{5 π}{7}

t = \frac{1}{1 - c o s \frac{5 π}{7}}

I H = \sqrt{x^{2} + x^{2} - 2 x^{2} c o s \frac{3 π}{7}}

= \sqrt{t (1 - c o s \frac{3 π}{7})}

= \sqrt{\frac{1 - c o s \frac{3 π}{7}}{1 - c o s \frac{5 π}{7}}}

Commented by M±th+et£s last updated on 01/Feb/20

n i c e w o r k s i r

Answered by mr W last updated on 01/Feb/20

Commented by mr W last updated on 01/Feb/20

α = \frac{π}{7}

A P = A B \times \sin α = \sin α

P L = \frac{A P}{\tan 2 α} = \frac{\sin α}{\tan 2 α}

H I = K L = 2 P L = \frac{2 \sin α}{\tan 2 α} = \frac{2 \sin \frac{π}{7}}{\tan \frac{2 π}{7}} \approx 0.692

Commented by M±th+et£s last updated on 01/Feb/20

t h a n k y o u s i r