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: 04

\begin{array}{l} Gegeben: \\ Hypotenuse c [m] \\ Kathete b [m] \\ Gesucht: \\ Kathete a [m] \\ a = \sqrt{c^{2} - b^{2}} \\ Gegeben: \\ c = 5 m b = 4 m \\ Rechnung: \\ a = \sqrt{c^{2} - b^{2}} \\ c = 5 m \\ b = 4 m \\ a = \sqrt{(5 m)^{2} - (4 m)^{2}} \\ a = 3 m \\ \begin{matrix} c = \\ 5 m \\ 50 d m \\ 500 c m \\ 5 \cdot 10^{3} m m \\ 5 \cdot 10^{6} μ m \end{matrix} \begin{matrix} b = \\ 4 m \\ 40 d m \\ 400 c m \\ 4 \cdot 10^{3} m m \\ 4 \cdot 10^{6} μ m \end{matrix} \begin{matrix} a = \\ 3 m \\ 30 d m \\ 300 c m \\ 3 \cdot 10^{3} m m \\ 3 \cdot 10^{6} μ m \end{matrix} \end{array}