Bijzondere rechthoekige driehoeken
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}M = 16 \text{,}\) \(\angle K = 30\degree\) en \(\angle L = 90\degree \text{.}\)
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 \({L\kern{-.8pt}M \over 1} = {K\kern{-.8pt}L \over \sqrt{3}} = {K\kern{-.8pt}M \over 2} \text{.}\)
1p
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Dit geeft \(K\kern{-.8pt}L = {K\kern{-.8pt}M ⋅ \sqrt{3} \over 2} = {16 ⋅ \sqrt{3} \over 2} \text{.}\)
1p
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\(K\kern{-.8pt}L = 8 \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 14 \text{,}\) \(\angle K = 30\degree\) en \(\angle L = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(K\kern{-.8pt}M \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({L\kern{-.8pt}M \over 1} = {K\kern{-.8pt}L \over \sqrt{3}} = {K\kern{-.8pt}M \over 2} \text{.}\)
1p
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Dit geeft \(K\kern{-.8pt}M = {K\kern{-.8pt}L ⋅ 2 \over \sqrt{3}} = {14 ⋅ 2 \over \sqrt{3}} \text{.}\)
1p
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\(K\kern{-.8pt}M = {28 \over \sqrt{3}} = 9\frac{1}{3} \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 11 \text{,}\) \(\angle C = 45\degree\) en \(\angle A = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(A\kern{-.8pt}C \text{.}\)
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In de bijzondere 45-45-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over \sqrt{2}} \text{.}\)
1p
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Dit geeft \(A\kern{-.8pt}C = {B\kern{-.8pt}C ⋅ 1 \over \sqrt{2}} = {11 ⋅ 1 \over \sqrt{2}} \text{.}\)
1p
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\(A\kern{-.8pt}C = {11 \over \sqrt{2}} = 5\frac{1}{2} \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 10 \text{,}\) \(\angle C = 45\degree\) 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 \({A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over \sqrt{2}} \text{.}\)
1p
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Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}C ⋅ \sqrt{2} \over 1} = {10 ⋅ \sqrt{2} \over 1} \text{.}\)
1p
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\(B\kern{-.8pt}C = 10 \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 22 \text{,}\) \(\angle B = 60\degree\) en \(\angle C = 90\degree \text{.}\)
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 \({B\kern{-.8pt}C \over 1} = {A\kern{-.8pt}C \over \sqrt{3}} = {A\kern{-.8pt}B \over 2} \text{.}\)
1p
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Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}B ⋅ 1 \over 2} = {22 ⋅ 1 \over 2} \text{.}\)
1p
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\(B\kern{-.8pt}C = 11 \text{.}\)
1p
3p
Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(P\kern{-.8pt}Q = 19 \text{,}\) \(\angle P = 60\degree\) en \(\angle Q = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(P\kern{-.8pt}R \text{.}\)
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In de bijzondere 30-60-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {Q\kern{-.8pt}R \over \sqrt{3}} = {P\kern{-.8pt}R \over 2} \text{.}\)
1p
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Dit geeft \(P\kern{-.8pt}R = {P\kern{-.8pt}Q ⋅ 2 \over 1} = {19 ⋅ 2 \over 1} \text{.}\)
1p
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\(P\kern{-.8pt}R = 38 \text{.}\)
1p