Bijzondere rechthoekige driehoeken
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 26 \text{,}\) \(\angle L = 30\degree\) en \(\angle M = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(L\kern{-.8pt}M \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({K\kern{-.8pt}M \over 1} = {L\kern{-.8pt}M \over \sqrt{3}} = {K\kern{-.8pt}L \over 2} \text{.}\)
1p
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Dit geeft \(L\kern{-.8pt}M = {K\kern{-.8pt}L ⋅ \sqrt{3} \over 2} = {26 ⋅ \sqrt{3} \over 2} \text{.}\)
1p
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\(L\kern{-.8pt}M = 13 \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 28 \text{,}\) \(\angle L = 30\degree\) en \(\angle M = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(K\kern{-.8pt}L \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({K\kern{-.8pt}M \over 1} = {L\kern{-.8pt}M \over \sqrt{3}} = {K\kern{-.8pt}L \over 2} \text{.}\)
1p
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Dit geeft \(K\kern{-.8pt}L = {L\kern{-.8pt}M ⋅ 2 \over \sqrt{3}} = {28 ⋅ 2 \over \sqrt{3}} \text{.}\)
1p
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\(K\kern{-.8pt}L = {56 \over \sqrt{3}} = 18\frac{2}{3} \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}R = 13 \text{,}\) \(\angle P = 45\degree\) en \(\angle Q = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(P\kern{-.8pt}Q \text{.}\)
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In de bijzondere 45-45-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {Q\kern{-.8pt}R \over 1} = {P\kern{-.8pt}R \over \sqrt{2}} \text{.}\)
1p
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Dit geeft \(P\kern{-.8pt}Q = {P\kern{-.8pt}R ⋅ 1 \over \sqrt{2}} = {13 ⋅ 1 \over \sqrt{2}} \text{.}\)
1p
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\(P\kern{-.8pt}Q = {13 \over \sqrt{2}} = 6\frac{1}{2} \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 17 \text{,}\) \(\angle A = 45\degree\) en \(\angle B = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(A\kern{-.8pt}C \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over 1} = {A\kern{-.8pt}C \over \sqrt{2}} \text{.}\)
1p
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Dit geeft \(A\kern{-.8pt}C = {A\kern{-.8pt}B ⋅ \sqrt{2} \over 1} = {17 ⋅ \sqrt{2} \over 1} \text{.}\)
1p
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\(A\kern{-.8pt}C = 17 \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 19 \text{,}\) \(\angle A = 60\degree\) en \(\angle B = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(A\kern{-.8pt}B \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over \sqrt{3}} = {A\kern{-.8pt}C \over 2} \text{.}\)
1p
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Dit geeft \(A\kern{-.8pt}B = {A\kern{-.8pt}C ⋅ 1 \over 2} = {19 ⋅ 1 \over 2} \text{.}\)
1p
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\(A\kern{-.8pt}B = 9\frac{1}{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 19 \text{,}\) \(\angle C = 60\degree\) en \(\angle A = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(B\kern{-.8pt}C \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over \sqrt{3}} = {B\kern{-.8pt}C \over 2} \text{.}\)
1p
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Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}C ⋅ 2 \over 1} = {19 ⋅ 2 \over 1} \text{.}\)
1p
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\(B\kern{-.8pt}C = 38 \text{.}\)
1p