Getal & Ruimte (13e editie) - 3 vwo
'Stelling van Pythagoras'.
| 2 vwo | 6.2 Schuine zijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 13 \text{,}\) \(P\kern{-.8pt}Q = 15\) 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 ○ \(Q\kern{-.8pt}R^{2} = 13^{2} + 15^{2} = 394 \text{.}\) 1p ○ \(Q\kern{-.8pt}R = \sqrt{394} ≈ 19{,}8 \text{.}\) 1p |
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| 2 vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q = 49 \text{,}\) \(P\kern{-.8pt}R = 55\) en \(\angle \text{Q} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(Q\kern{-.8pt}R \text{.}\) Pythagoras (2) 007d - Stelling van Pythagoras - basis - 0ms ○ Pythagoras in \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geeft \(P\kern{-.8pt}Q^{2} + Q\kern{-.8pt}R^{2} = P\kern{-.8pt}R^{2}\) ofwel \(49^{2} + Q\kern{-.8pt}R^{2} = 55^{2} \text{.}\) 1p ○ \(Q\kern{-.8pt}R^{2} = 55^{2} - 49^{2} = 624 \text{.}\) 1p ○ \(Q\kern{-.8pt}R = \sqrt{624} ≈ 25{,}0 \text{.}\) 1p |