Getal & Ruimte (13e editie) - 3 havo
'Stelling van Pythagoras'.
| 2 havo/vwo | 6.2 Schuine zijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q = 54 \text{,}\) \(Q\kern{-.8pt}R = 29\) en \(\angle \text{Q} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}R \text{.}\) Pythagoras (1) 007c - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(P\kern{-.8pt}Q^{2} + Q\kern{-.8pt}R^{2} = P\kern{-.8pt}R^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}R^{2} = 54^{2} + 29^{2} = 3\,757 \text{.}\) 1p ○ \(P\kern{-.8pt}R = \sqrt{3\,757} ≈ 61{,}3 \text{.}\) 1p |
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| 2 havo/vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 32 \text{,}\) \(Q\kern{-.8pt}R = 39\) 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 \(32^{2} + P\kern{-.8pt}Q^{2} = 39^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}Q^{2} = 39^{2} - 32^{2} = 497 \text{.}\) 1p ○ \(P\kern{-.8pt}Q = \sqrt{497} ≈ 22{,}3 \text{.}\) 1p |