Triangle Questions (1 Viewer)

philly2000 · Feb 28, 2009

Hey all, can you help me with q 2) c) and 3) iii), thanks!

kurt.physics · Feb 28, 2009

philly2000 said:
Hey all, can you help me with q 2) c) and 3) iii), thanks!

2c) Use ratio of intercepts.

we have from (a)

$\frac{BC}{DE} = \frac{AB}{AD} = \frac{3}{3 + 5} = \frac{3}{8}$

ie $BC:DE = 3:8$

Also, from (b)

$\frac{DF}{FC} = \frac{DE}{BC} = \frac{8}{3}$

ie

$DF:FC = 8:3$

philly2000 · Feb 28, 2009

thanks kurt.physics!
think my brain is dying... it was so simple

gurmies · Feb 28, 2009

i

$\sin A = \frac{CD}{b}$

$\therefore CD = b\sin A$

$\sin B = \frac{CD}{a}$

$CD = a\sin B$

$\therefore a\sin B = b\sin A$

ii

$\cos A = \frac{AD}{b}$

$\therefore AD = b\cos A$

$\cos B = \frac{BD}{a}$

$\therefore BD = a\cos B$

$AD + BD = c$

$\therefore c = a\cos B + b\cos A$

iii

$c^{2} = 4ab \cos A \cos B$

$c^{2} = a^{2}\cos^{2}B + 2ab \cos A \cos B + b^{2}\cos^{2}A$

$a^{2}\cos^{2}B - 2ab \cos A \cos B + b^{2}\cos^{2}A = 0$

$(a\cos B - b\cos A)^{2} = 0$

$a\cos B = b\cos A$

$Now, \,\,\, we \,\,\, know \,\,\, that \,\,\, a\sin B = b\sin A$

$Dividing \,\,\, by \,\,\, a\cos B \,\,\,and\,\,\, b\cos A$

$\tan A = \tan B$

$\therefore A = B$

$\therefore a = b$

kurt.physics · Feb 28, 2009

gurmies said:
iii

...

$a\cos B = b\cos A$

$Now, \,\,\, we \,\,\, know \,\,\, that \,\,\, a\sin B = b\sin A$

$Dividing \,\,\, by \,\,\, a\cos B \,\,\,and\,\,\, b\cos A$

$\tan A = \tan B$

...

Hey Gurmies, this is a wicked solution, but i don't really understand the bit i quoted. Could you please explain.

Trebla · Feb 28, 2009

a sin B = b sin A, because of the sine rule: (sin B)/b = (sin A)/a

kurt.physics · Feb 28, 2009

Trebla said:
a sin B = b sin A, because of the sine rule: (sin B)/b = (sin A)/a

i get this but the dividing part i dont get

lyounamu · Feb 28, 2009

kurt.physics said:
i get this but the dividing part i dont get

Since they are same, they can be used to be divided by acos B = b cosA, leaving tan B = tan A only.

kurt.physics · Feb 28, 2009

Ohhh :S

I get it know...

Thanks

looks like my brain is dying too...

gurmies · Mar 1, 2009

Sorry I was unavailable to explain that myself Kurt, but the others did a fine job =)

Oh Trebla, that saves quite a bit of time...can't believe I didn't see that

philly2000 · Mar 1, 2009

thanks guys, appreciate the help

Triangle Questions (1 Viewer)

philly2000

New Member

kurt.physics

Member

philly2000

New Member

gurmies

Drover

kurt.physics

Member

Trebla

Administrator

kurt.physics

Member

lyounamu

Reborn

kurt.physics

Member

gurmies

Drover

philly2000

New Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)