Stelling van Pythagoras
13 - 2 oefeningen
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Pythagoras (1)
007c - Stelling van Pythagoras - basis - 0ms
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Getal & Ruimte (13e editie) - 2 havo/vwo - 6.2 Getal & Ruimte (13e editie) - 2 vwo - 6.2 Moderne Wiskunde (13e editie) - 2 vmbo k(gt) - 7.3 |
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Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 23 \text{,}\) \(P\kern{-.8pt}R = 24\) en \(\angle \text{R} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}Q \text{.}\) |
○ 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 ○ \(P\kern{-.8pt}Q^{2} = 23^{2} + 24^{2} = 1\,105 \text{.}\) 1p ○ \(P\kern{-.8pt}Q = \sqrt{1\,105} ≈ 33{,}2 \text{.}\) 1p |
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Pythagoras (2)
007d - Stelling van Pythagoras - basis - 0ms
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Getal & Ruimte (13e editie) - 2 havo/vwo - 6.3 Getal & Ruimte (13e editie) - 2 vwo - 6.3 Moderne Wiskunde (13e editie) - 2 vmbo k(gt) - 7.4 |
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Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 11 \text{,}\) \(P\kern{-.8pt}Q = 16\) en \(\angle \text{R} = 90\degree \text{.}\) 3p Bereken de lengte van zijde \(P\kern{-.8pt}R \text{.}\) |
○ 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 \(11^{2} + P\kern{-.8pt}R^{2} = 16^{2} \text{.}\) 1p ○ \(P\kern{-.8pt}R^{2} = 16^{2} - 11^{2} = 135 \text{.}\) 1p ○ \(P\kern{-.8pt}R = \sqrt{135} ≈ 11{,}6 \text{.}\) 1p |