3p
Gegeven is \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) met \(Q\kern{-.8pt}R = 24 \text{,}\) \(\angle R = 30\degree\) en \(\angle P = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(P\kern{-.8pt}R \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {P\kern{-.8pt}R \over \sqrt{3}} = {Q\kern{-.8pt}R \over 2} \text{.}\)
1p
○
Dit geeft \(P\kern{-.8pt}R = {Q\kern{-.8pt}R ⋅ \sqrt{3} \over 2} = {24 ⋅ \sqrt{3} \over 2} \text{.}\)
1p
○
\(P\kern{-.8pt}R = 12 \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 16 \text{,}\) \(\angle K = 30\degree\) en \(\angle L = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(K\kern{-.8pt}M \text{.}\)
○
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
○
Dit geeft \(K\kern{-.8pt}M = {K\kern{-.8pt}L ⋅ 2 \over \sqrt{3}} = {16 ⋅ 2 \over \sqrt{3}} \text{.}\)
1p
○
\(K\kern{-.8pt}M = {32 \over \sqrt{3}} = 10\frac{2}{3} \sqrt{3} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(K\kern{-.8pt}L = 17 \text{,}\) \(\angle L = 45\degree\) en \(\angle M = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(L\kern{-.8pt}M \text{.}\)
○
In de bijzondere 45-45-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({L\kern{-.8pt}M \over 1} = {K\kern{-.8pt}M \over 1} = {K\kern{-.8pt}L \over \sqrt{2}} \text{.}\)
1p
○
Dit geeft \(L\kern{-.8pt}M = {K\kern{-.8pt}L ⋅ 1 \over \sqrt{2}} = {17 ⋅ 1 \over \sqrt{2}} \text{.}\)
1p
○
\(L\kern{-.8pt}M = {17 \over \sqrt{2}} = 8\frac{1}{2} \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) met \(B\kern{-.8pt}C = 23 \text{,}\) \(\angle B = 45\degree\) 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 \(A\kern{-.8pt}B = {B\kern{-.8pt}C ⋅ \sqrt{2} \over 1} = {23 ⋅ \sqrt{2} \over 1} \text{.}\)
1p
○
\(A\kern{-.8pt}B = 23 \sqrt{2} \text{.}\)
1p
3p
Gegeven is \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) met \(L\kern{-.8pt}M = 29 \text{,}\) \(\angle M = 60\degree\) en \(\angle K = 90\degree \text{.}\)
Bereken exact de lengte van zijde \(K\kern{-.8pt}M \text{.}\)
○
In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({K\kern{-.8pt}M \over 1} = {K\kern{-.8pt}L \over \sqrt{3}} = {L\kern{-.8pt}M \over 2} \text{.}\)
1p
○
Dit geeft \(K\kern{-.8pt}M = {L\kern{-.8pt}M ⋅ 1 \over 2} = {29 ⋅ 1 \over 2} \text{.}\)
1p
○
\(K\kern{-.8pt}M = 14\frac{1}{2} \text{.}\)
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 \(B\kern{-.8pt}C \text{.}\)
○
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
○
Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}C ⋅ 2 \over 1} = {19 ⋅ 2 \over 1} \text{.}\)
1p
○
\(B\kern{-.8pt}C = 38 \text{.}\)
1p