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: 11

\begin{array}{l} Gegeben: \\ Kathete b [m] \\ Fläche des Dreiecks A [m^{2}] \\ Gesucht: \\ Gegenkathete zu α a [m] \\ a = \frac{A \cdot 2}{b} \\ Gegeben: \\ b = 1 \frac{1}{5} m A = 1 \frac{1}{2} m^{2} \\ Rechnung: \\ a = \frac{A \cdot 2}{b} \\ b = 1 \frac{1}{5} m \\ A = 1 \frac{1}{2} m^{2} \\ a = \frac{1 \frac{1}{2} m^{2} \cdot 2}{1 \frac{1}{5} m} \\ a = 2 \frac{1}{2} m \\ \begin{matrix} b = \\ 1 \frac{1}{5} m \\ 12 d m \\ 120 c m \\ 1, 2 \cdot 10^{3} m m \\ 1, 2 \cdot 10^{6} μ m \end{matrix} \begin{matrix} A = \\ 1 \frac{1}{2} m^{2} \\ 150 d m^{2} \\ 1, 5 \cdot 10^{4} c m^{2} \\ 1, 5 \cdot 10^{6} m m^{2} \\ 0, 015 a \\ 0, 00015 h a \end{matrix} \begin{matrix} a = \\ 2 \frac{1}{2} m \\ 25 d m \\ 250 c m \\ 2, 5 \cdot 10^{3} m m \\ 2, 5 \cdot 10^{6} μ m \end{matrix} \end{array}