• 2. Strahlensatz Übungen
  • Deliah Herbstritt
  • 21.07.2020
  • Mathematik
  • Flächen
  • R
  • 9
  • Einzelarbeit
  • Arbeitsblatt
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1
Wie lang ist X?
Lösung1
CADB=SCSD\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline {CA}}{\overline{DB}}=\frac{\overline{SC}}{\overline{SD}}

X5,32=4,55cm4,55cm+6,50cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{X}{5{,}32} = \frac{4{,}55cm}{4{,}55cm+6{,}50cm} 5,32cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot5{,}32cm

X=4,55cm11,05cm5,32cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X=\frac{4{,}55cm}{11{,}05cm}\cdot5{,}32cm

X2,19cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X\approx2{,}19cm

Antwort: Die Strecke X ist 2,19cm lang.
Hinweis

Du kannst auch den 1. Strahlensatz anwenden, um die Lösung herauszufinden.

2
Wie lang ist X?
Lösung2
BDAC=SDSC\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline{BD}}{\overline{AC}}=\frac{\overline{SD}}{\overline{SC}}

X4cm=2cm+2,86cm2cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{X}{4cm}=\frac{2cm+2{,}86cm}{2cm} 4cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot4cm

X=4,86cm2cm4cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X=\frac{4{,}86cm}{2cm}\cdot4cm

X=9,72cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X=9{,}72cm

Antwort: Die Strecke X ist 9,72cm lang.
3
Wie lange sind x und y?
Lösung x3
SDSC=DBCA\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline{SD}}{\overline{SC}}=\frac{\overline{DB}}{\overline{CA}}

2,86cm+X2,86cm=10cm4,11cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{2{,}86cm+X}{2{,}86cm}=\frac{10cm}{4{,}11cm} 2,86cm2,86cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot2{,}86cm |-2{,}86cm

X=10cm4,11cm2,862,86cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X=\frac{10cm}{4{,}11cm}\cdot2{,}86-2{,}86cm

X4,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} X\approx4{,}1cm

Antwort: Die Strecke X ist 4,1cm läng.
Lösung y
SAAB=SCCD\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline{SA}}{\overline{AB}}=\frac{\overline{SC}}{\overline{CD}}

y3cm=2,86cm4,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{y}{3cm}=\frac{2{,}86cm}{4{,}1cm} 3cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot3cm

y=2,86cm4,1cm3cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} y=\frac{2{,}86cm}{4{,}1cm}\cdot3cm

y2,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} y\approx2{,}1cm

Antwort: Die Strecke y ist 2,1cm lang.
4
Wie lang sind x und y?
Lösung x4
SAAB=SCCD\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline{SA}}{\overline{AB}}=\frac{\overline{SC}}{\overline{CD}}

x4,41cm=1,6cm2,28cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{x}{4{,}41cm}=\frac{1{,}6cm}{2{,}28cm} 4,41cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot4{,}41cm

x=1,6cm2,28cm4,41cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} x=\frac{1{,}6cm}{2{,}28cm}\cdot4{,}41cm

y3,09cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} y\approx3{,}09cm

Antwort: Die Strecke y ist 3,09cm lang.
Lösung y
ACBD=SCSD\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{\overline{AC}}{\overline{BD}}=\frac{\overline{SC}}{\overline{SD}}

y4,95cm=1,6cm3,88cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \frac{y}{4{,}95cm}=\frac{1{,}6cm}{3{,}88cm} 4,95cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} |\cdot4{,}95cm

y=1,6cm3,88cm4,95cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} y=\frac{1{,}6cm}{3{,}88cm}\cdot4{,}95cm

y2,04cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} y\approx2{,}04cm

Antwort: Die Strecke y ist 2,04cm lang.