Den vilkårlige trekant matematik opg

Aflevering om den vilkårlige trekant.

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Indholdsfortegnelse

1 Opg. 9
2 Opg. 11
3 12
4 13

Opg. 9

C = 30
b = 10
c = 7
B = Sin^-1(Sin(C)*(b/c)) =

Opg. 11

$LaTex: \angle CDB = 50^o$
$LaTex: \angle CDA = 85^o$
$LaTex: \angle BDA = 85^o-50^o=35^o$
$LaTex: |CD| = 25 m$
$LaTex: |BD| = 39 m$
$LaTex: |AD| = 42 m$

$LaTex: |BC| = sqrt{|BD|^2+|CD|^2-2\times |BD|\times|CD|\times\cos(\angle CDB)}=29,9 m$

$LaTex: \angle BCD = \cos^{-1}\left(\frac{|BC|^2+|CD|^2-|BD|^2}{2\times|BC|\times|CD|}\right)=90^o$

$LaTex: \angle CBD = \cos^{-1}\left(\frac{|BC|^2+|BD|^2-|CD|^2}{2\times|BC|\times|BD|}\right)=39,9^o$

$LaTex: |AB| = sqrt{|BD|^2+|AD|^2-2\times|BD|\times|AD|\times\cos(\angle BDA)}=24,5 m$

$LaTex: \angle DAB = \cos^{-1}\left(\frac{|AB|^2+|AD|^2-|BD|^2}{2\times|AD|\times|AB|}\right)=65,8^o$

$LaTex: \angle ABD = 360-(\angle DAB+\angle BDA)=79,2^o$

$LaTex: X_D = 1000$
$LaTex: Y_D = 1000$

$LaTex: X_A = X_D-|AD| = 958$
$LaTex: Y_A = Y_D = 1000$

$LaTex: X_C = X_D-sqrt{|CD|^2-(\sin(\angle CDA)\times |CD|)^2}=997,8$
$LaTex: Y_C = Y_D+\sin(\angle CDA)\times |CD| = 1019,5$

$LaTex: X_B = X_D-sqrt{|BD|^2-(\sin(\angle BDA)\times |BD|)^2} = 968$
$LaTex: Y_B = Y_D+\sin(\angle BDA)\times |BD| = 1022,3$

$LaTex: Areal_{Firkant} = 0,5\times |CD|\times |BC|\times \sin(\angle BCD)+0,5\times |AB|\times |BD|\times \sin(\angle ABD)\\ = 843,03 m^2$

12

$LaTex: A_{stang} = 400*16 = 6400$

$LaTex: A_{firkant} = 40\times(110-(40+16))=2160$

$LaTex: A_{indrundning} = 20^2-\frac{20^2\times\pi}{4}=400-100\times\pi \approx 85,8$

$LaTex: A_{udrundning} = \frac{40^2\times\pi}{4} = 400\times\pi \approx 1256,6$

$LaTex: A_{trekant} = \frac{\tan(10)\times (110-(20+16+40))^2}{2} = 578\times\tan(10) \approx 101,9$

$LaTex: A_{lille firkant} = \tan(10)\times (110-(20+16+40)) \times 20 = 680\times\tan(10) \approx 119,9$

$LaTex: A_{fod} = A_{firkant}+A_{indrundning}+A_{udrundning}+A_{trekant}+A_{lille firkant}\\=1258\times\tan(10)+300\times\pi+2560 \approx 3724,3$

$LaTex: A_{figur} = 2\times A_{fod}+A_{stang}=\frac{4\times(30\times\cos(10)\times(5\times\pi+96)+629\times\sin(10))}{\cos(10)} \approx 13848,6$

13

log(x-a)*2+log(y-b)*2=log(r)*2

Hentet fra "http://jopsen.dk/wiki/Den_vilk%C3%A5rlige_trekant_matematik_opg/"

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