Getal & Ruimte (13e editie) - vwo wiskunde B
'Stelling van Pythagoras'.
| 2 vwo | 6.2 Schuine zijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 44 \text{,}\) \(P\kern{-.8pt}R = 40\) en \(\angle \text{R} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}Q \text{.}\) Pythagoras (1) 007c - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(Q\kern{-.8pt}R^{2} + P\kern{-.8pt}R^{2} = P\kern{-.8pt}Q^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}Q^{2} = 44^{2} + 40^{2} = 3\,536 \text{.}\) 1p ○ \(P\kern{-.8pt}Q = \sqrt{3\,536} ≈ 59{,}5 \text{.}\) 1p |
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| 2 vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 16 \text{,}\) \(P\kern{-.8pt}Q = 30\) 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 \(16^{2} + P\kern{-.8pt}R^{2} = 30^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}R^{2} = 30^{2} - 16^{2} = 644 \text{.}\) 1p ○ \(P\kern{-.8pt}R = \sqrt{644} ≈ 25{,}4 \text{.}\) 1p |