Ein rechtwinkliges Dreieck hat eine Kathete, die 8 Einheiten und eine Hypotenuse, die 10 Einheiten misst. Wie lang ist die andere Kathete?
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- Die Formel für die maximale Höhe lautet \( h = \frac{v_0^2}{2g} \).
- Einsetzen der Werte: \( h = \frac{20^2}{2 \times 9,8} = \frac{400}{19,6} = 20,4 \) Meter.
- #### 20,4 Meter
- Verwendung des Satzes des Pythagoras: \( a^2 + b^2 = c^2 \), wobei \( a = 8 \) und \( c = 10 \).
- Also, \( 8^2 + b^2 = 10^2 \), was sich vereinfacht zu \( 64 + b^2 = 100 \).
- Auflösen nach \( b \): \( b^2 = 100 - 64 = 36 \), also \( b = \sqrt{36} = 6 \) Einheiten.
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