Bijzondere rechthoekige driehoeken

In de bijzondere 30-60-90 driehoek \(\triangle K\kern{-.8pt}L\kern{-.8pt}M\) geldt \({L\kern{-.8pt}M \over 1} = {K\kern{-.8pt}L \over \sqrt{3}} = {K\kern{-.8pt}M \over 2} \text{.}\)

Dit geeft \(K\kern{-.8pt}L = {K\kern{-.8pt}M ⋅ \sqrt{3} \over 2} = {25 ⋅ \sqrt{3} \over 2} \text{.}\)

\(K\kern{-.8pt}L = 12\frac{1}{2} \sqrt{3} \text{.}\)

In de bijzondere 30-60-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {P\kern{-.8pt}R \over \sqrt{3}} = {Q\kern{-.8pt}R \over 2} \text{.}\)

Dit geeft \(Q\kern{-.8pt}R = {P\kern{-.8pt}R ⋅ 2 \over \sqrt{3}} = {16 ⋅ 2 \over \sqrt{3}} \text{.}\)

\(Q\kern{-.8pt}R = {32 \over \sqrt{3}} = 10\frac{2}{3} \sqrt{3} \text{.}\)

In de bijzondere 45-45-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {Q\kern{-.8pt}R \over 1} = {P\kern{-.8pt}R \over \sqrt{2}} \text{.}\)

Dit geeft \(P\kern{-.8pt}Q = {P\kern{-.8pt}R ⋅ 1 \over \sqrt{2}} = {27 ⋅ 1 \over \sqrt{2}} \text{.}\)

\(P\kern{-.8pt}Q = {27 \over \sqrt{2}} = 13\frac{1}{2} \sqrt{2} \text{.}\)

In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}C \over 1} = {A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over \sqrt{2}} \text{.}\)

Dit geeft \(B\kern{-.8pt}C = {A\kern{-.8pt}C ⋅ \sqrt{2} \over 1} = {19 ⋅ \sqrt{2} \over 1} \text{.}\)

\(B\kern{-.8pt}C = 19 \sqrt{2} \text{.}\)

In de bijzondere 30-60-90 driehoek \(\triangle A\kern{-.8pt}B\kern{-.8pt}C\) geldt \({A\kern{-.8pt}B \over 1} = {B\kern{-.8pt}C \over \sqrt{3}} = {A\kern{-.8pt}C \over 2} \text{.}\)

Dit geeft \(A\kern{-.8pt}B = {A\kern{-.8pt}C ⋅ 1 \over 2} = {10 ⋅ 1 \over 2} \text{.}\)

\(A\kern{-.8pt}B = 5 \text{.}\)

In de bijzondere 30-60-90 driehoek \(\triangle P\kern{-.8pt}Q\kern{-.8pt}R\) geldt \({P\kern{-.8pt}Q \over 1} = {Q\kern{-.8pt}R \over \sqrt{3}} = {P\kern{-.8pt}R \over 2} \text{.}\)

Dit geeft \(P\kern{-.8pt}R = {P\kern{-.8pt}Q ⋅ 2 \over 1} = {24 ⋅ 2 \over 1} \text{.}\)

\(P\kern{-.8pt}R = 48 \text{.}\)