Getal & Ruimte (13e editie) - 2 havo/vwo
'Stelling van Pythagoras'.
| 2 havo/vwo | 6.2 Schuine zijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 52 \text{,}\) \(P\kern{-.8pt}Q = 12\) en \(\angle \text{P} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(Q\kern{-.8pt}R \text{.}\) Pythagoras (1) 007c - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(P\kern{-.8pt}R^{2} + P\kern{-.8pt}Q^{2} = Q\kern{-.8pt}R^{2} \text{.}\) 1p ○ \(Q\kern{-.8pt}R^{2} = 52^{2} + 12^{2} = 2\,848 \text{.}\) 1p ○ \(Q\kern{-.8pt}R = \sqrt{2\,848} ≈ 53{,}4 \text{.}\) 1p |
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| 2 havo/vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 25 \text{,}\) \(Q\kern{-.8pt}R = 33\) en \(\angle \text{P} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}Q \text{.}\) Pythagoras (2) 007d - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(P\kern{-.8pt}R^{2} + P\kern{-.8pt}Q^{2} = Q\kern{-.8pt}R^{2}\) ofwel \(25^{2} + P\kern{-.8pt}Q^{2} = 33^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}Q^{2} = 33^{2} - 25^{2} = 464 \text{.}\) 1p ○ \(P\kern{-.8pt}Q = \sqrt{464} ≈ 21{,}5 \text{.}\) 1p |