Getal & Ruimte (12e 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 \(P\kern{-.8pt}R = 35 \text{,}\) \(P\kern{-.8pt}Q = 11\) 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 ○ \(Q\kern{-.8pt}R^{2} = 35^{2} + 11^{2} = 1\,346 \text{.}\) 1p ○ \(Q\kern{-.8pt}R = \sqrt{1\,346} ≈ 36{,}7 \text{.}\) 1p |
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| 2 vwo | 6.3 Rechthoekszijden berekenen |
opgave 1Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 55 \text{,}\) \(P\kern{-.8pt}Q = 76\) 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 \(55^{2} + P\kern{-.8pt}R^{2} = 76^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}R^{2} = 76^{2} - 55^{2} = 2\,751 \text{.}\) 1p ○ \(P\kern{-.8pt}R = \sqrt{2\,751} ≈ 52{,}4 \text{.}\) 1p |