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 \(\triangle ABC\) met \(BC=54\text{,}\) \(AC=31\) en \(\angle C=90\degree\text{.}\) |
a Pythagoras in \(\triangle ABC\) geeft \(BC^2+AC^2=AB^2\text{.}\) 1p \(AB^2=54^2+31^2=3\,877\text{.}\) 1p \(AB=\sqrt{3\,877}≈62{,}3\text{.}\) 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 \(\triangle PQR\) met \(QR=34\text{,}\) \(PQ=43\) en \(\angle R=90\degree\text{.}\) |
a Pythagoras in \(\triangle PQR\) geeft \(QR^2+PR^2=PQ^2\) ofwel \(34^2+PR^2=43^2\text{.}\) 1p \(PR^2=43^2-34^2=693\text{.}\) 1p \(PR=\sqrt{693}≈26{,}3\text{.}\) 1p |