Beispielaufgaben Geometrie - Dreieck - Rechtwinkliges Dreieck

A = \frac{a \cdot b}{2}

a = \frac{A \cdot 2}{b}

b = \frac{A \cdot 2}{a}

c = \sqrt{a^{2} + b^{2}}

a = \sqrt{c^{2} - b^{2}}

b = \sqrt{c^{2} - a^{2}}

h = \sqrt{p \cdot q}

q = \frac{h^{2}}{p}

p = \frac{h^{2}}{q}

a = \sqrt{c \cdot p}

c = \frac{a^{2}}{p}

p = \frac{a^{2}}{c}

Geometrie-Dreieck-Rechtwinkliges Dreieck

A = \frac{a \cdot b}{2}

1 2 3 4 5 6 7 8 9 10 11 12

a = \frac{A \cdot 2}{b}

1 2 3 4 5 6 7 8 9 10 11 12

b = \frac{A \cdot 2}{a}

1 2 3 4 5 6 7 8 9 10 11 12

a^{2} + b^{2} = c^{2}

c = \sqrt{a^{2} + b^{2}}

1 2 3 4 5 6 7 8 9 10 11 12

a = \sqrt{c^{2} - b^{2}}

1 2 3 4 5 6 7 8 9 10

b = \sqrt{c^{2} - a^{2}}

1 2 3 4 5

h^{2} = p \cdot q

h = \sqrt{p \cdot q}

1 2 3 4

q = \frac{h^{2}}{p}

1 2 3 4

p = \frac{h^{2}}{q}

1 2 3

a^{2} = c \cdot p b^{2} = c \cdot q

a = \sqrt{c \cdot p}

1 2 3

c = \frac{a^{2}}{p}

1 2 3 4

p = \frac{a^{2}}{c}

1 2 3 4

Beispiel Nr: 09

\begin{array}{l} Gegeben: \\ Hypotenuse c [m] \\ Kathete b [m] \\ Gesucht: \\ Kathete a [m] \\ a = \sqrt{c^{2} - b^{2}} \\ Gegeben: \\ c = 10 m b = 6 m \\ Rechnung: \\ a = \sqrt{c^{2} - b^{2}} \\ c = 10 m \\ b = 6 m \\ a = \sqrt{(10 m)^{2} - (6 m)^{2}} \\ a = 8 m \\ \begin{matrix} c = \\ 10 m \\ 100 d m \\ 10^{3} c m \\ 10^{4} m m \\ 10^{7} μ m \end{matrix} \begin{matrix} b = \\ 6 m \\ 60 d m \\ 600 c m \\ 6 \cdot 10^{3} m m \\ 6 \cdot 10^{6} μ m \end{matrix} \begin{matrix} a = \\ 8 m \\ 80 d m \\ 800 c m \\ 8 \cdot 10^{3} m m \\ 8 \cdot 10^{6} μ m \end{matrix} \end{array}