Bijzondere rechthoekige driehoeken

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

Dit geeft \(A\kern{-.8pt}B={A\kern{-.8pt}C⋅\sqrt{3} \over 2}={30⋅\sqrt{3} \over 2}\text{.}\)

\(A\kern{-.8pt}B=15\sqrt{3}\text{.}\)

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

Dit geeft \(K\kern{-.8pt}M={K\kern{-.8pt}L⋅2 \over \sqrt{3}}={23⋅2 \over \sqrt{3}}\text{.}\)

\(K\kern{-.8pt}M={46 \over \sqrt{3}}=15\frac{1}{3}\sqrt{3}\text{.}\)

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 \(P\kern{-.8pt}Q={P\kern{-.8pt}R⋅1 \over \sqrt{2}}={25⋅1 \over \sqrt{2}}\text{.}\)

\(P\kern{-.8pt}Q={25 \over \sqrt{2}}=12\frac{1}{2}\sqrt{2}\text{.}\)

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 \(B\kern{-.8pt}C={A\kern{-.8pt}C⋅\sqrt{2} \over 1}={12⋅\sqrt{2} \over 1}\text{.}\)

\(B\kern{-.8pt}C=12\sqrt{2}\text{.}\)

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

Dit geeft \(Q\kern{-.8pt}R={P\kern{-.8pt}Q⋅1 \over 2}={20⋅1 \over 2}\text{.}\)

\(Q\kern{-.8pt}R=10\text{.}\)

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

Dit geeft \(P\kern{-.8pt}Q={Q\kern{-.8pt}R⋅2 \over 1}={18⋅2 \over 1}\text{.}\)

\(P\kern{-.8pt}Q=36\text{.}\)