Stelling van Pythagoras
13 - 2 oefeningen
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Pythagoras (1)
007c - basis
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Getal & Ruimte (13e editie) - 2 havo/vwo - 6.2 Getal & Ruimte (13e editie) - 2 vwo - 6.2 |
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3p a Gegeven is \(\triangle PQR\) met \(PQ=16\text{,}\) \(QR=11\) en \(\angle Q=90\degree\text{.}\) |
a Pythagoras in \(\triangle PQR\) geeft \(PQ^2+QR^2=PR^2\text{.}\) 1p \(PR^2=16^2+11^2=377\text{.}\) 1p \(PR=\sqrt{377}≈19{,}4\text{.}\) 1p |
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Pythagoras (2)
007d - basis
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Getal & Ruimte (13e editie) - 2 havo/vwo - 6.3 Getal & Ruimte (13e editie) - 2 vwo - 6.3 |
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3p a Gegeven is \(\triangle ABC\) met \(AB=25\text{,}\) \(AC=57\) en \(\angle B=90\degree\text{.}\) |
a Pythagoras in \(\triangle ABC\) geeft \(AB^2+BC^2=AC^2\) ofwel \(25^2+BC^2=57^2\text{.}\) 1p \(BC^2=57^2-25^2=2\,624\text{.}\) 1p \(BC=\sqrt{2\,624}≈51{,}2\text{.}\) 1p |