Getal & Ruimte (13e editie) - 2 havo/vwo
'Stelling van Pythagoras'.
| 2 havo/vwo | 6.2 Schuine zijden berekenen |
opgave 1Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 25 \text{,}\) \(A\kern{-.8pt}C = 12\) en \(\angle \text{C} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(A\kern{-.8pt}B \text{.}\) Pythagoras (1) 007c - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geeft \(B\kern{-.8pt}C^{2} + A\kern{-.8pt}C^{2} = A\kern{-.8pt}B^{2} \text{.}\) 1p ○ \(A\kern{-.8pt}B^{2} = 25^{2} + 12^{2} = 769 \text{.}\) 1p ○ \(A\kern{-.8pt}B = \sqrt{769} ≈ 27{,}7 \text{.}\) 1p |
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| 2 havo/vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 55 \text{,}\) \(P\kern{-.8pt}Q = 70\) en \(\angle \text{R} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}R \text{.}\) Pythagoras (2) 007d - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(Q\kern{-.8pt}R^{2} + P\kern{-.8pt}R^{2} = P\kern{-.8pt}Q^{2}\) ofwel \(55^{2} + P\kern{-.8pt}R^{2} = 70^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}R^{2} = 70^{2} - 55^{2} = 1\,875 \text{.}\) 1p ○ \(P\kern{-.8pt}R = \sqrt{1\,875} ≈ 43{,}3 \text{.}\) 1p |