3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 22 \text{,}\) \(\angle L = 30\degree\) en \(\angle M = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(L\kern{-.8pt}M \text{.}\)
○
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 \(L\kern{-.8pt}M = {K\kern{-.8pt}L ⋅ \sqrt{3} \over 2} = {22 ⋅ \sqrt{3} \over 2} \text{.}\)
1p
○
\(L\kern{-.8pt}M = 11 \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}C = 10 \text{,}\) \(\angle C = 30\degree\) en \(\angle A = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(B\kern{-.8pt}C \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}B \over 1} = {A\kern{-.8pt}C \over \sqrt{3}} = {B\kern{-.8pt}C \over 2} \text{.}\)
1p
○
Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}C ⋅ 2 \over \sqrt{3}} = {10 ⋅ 2 \over \sqrt{3}} \text{.}\)
1p
○
\(B\kern{-.8pt}C = {20 \over \sqrt{3}} = 6\frac{2}{3} \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(A\kern{-.8pt}B = 24 \text{,}\) \(\angle B = 45\degree\) en \(\angle C = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(B\kern{-.8pt}C \text{.}\)
○
In de bijzondere 45-45-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({B\kern{-.8pt}C \over 1} = {A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over \sqrt{2}} \text{.}\)
1p
○
Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}B ⋅ 1 \over \sqrt{2}} = {24 ⋅ 1 \over \sqrt{2}} \text{.}\)
1p
○
\(B\kern{-.8pt}C = {24 \over \sqrt{2}} = 12 \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 18 \text{,}\) \(\angle B = 45\degree\) en \(\angle C = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(A\kern{-.8pt}B \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({B\kern{-.8pt}C \over 1} = {A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over \sqrt{2}} \text{.}\)
1p
○
Dit geeft \(A\kern{-.8pt}B = {B\kern{-.8pt}C ⋅ \sqrt{2} \over 1} = {18 ⋅ \sqrt{2} \over 1} \text{.}\)
1p
○
\(A\kern{-.8pt}B = 18 \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}M = 23 \text{,}\) \(\angle K = 60\degree\) en \(\angle L = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(K\kern{-.8pt}L \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({K\kern{-.8pt}L \over 1} = {L\kern{-.8pt}M \over \sqrt{3}} = {K\kern{-.8pt}M \over 2} \text{.}\)
1p
○
Dit geeft \(K\kern{-.8pt}L = {K\kern{-.8pt}M ⋅ 1 \over 2} = {23 ⋅ 1 \over 2} \text{.}\)
1p
○
\(K\kern{-.8pt}L = 11\frac{1}{2} \text{.}\)
1p
3p
Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 17 \text{,}\) \(\angle Q = 60\degree\) en \(\angle R = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(P\kern{-.8pt}Q \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({Q\kern{-.8pt}R \over 1} = {P\kern{-.8pt}R \over \sqrt{3}} = {P\kern{-.8pt}Q \over 2} \text{.}\)
1p
○
Dit geeft \(P\kern{-.8pt}Q = {Q\kern{-.8pt}R ⋅ 2 \over 1} = {17 ⋅ 2 \over 1} \text{.}\)
1p
○
\(P\kern{-.8pt}Q = 34 \text{.}\)
1p