Goniometrie

Bereken de grootte van de hoek(en) en de lengte van de zijde(n) in een rechthoekige driehoek

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\( a = \sqrt{4^2+12^2} \approx 12,649 \text{ (Pythagoras)} \\ \text{sin}(B)=\frac{4}{12,649} \Leftrightarrow B = \text{arcsin}(\frac{4}{12,649110640674}) \approx 18,435=18^\circ 26' 5,8" \text{ (Formule sinus)}\\ \text{sin}(C)=\frac{12}{12,649} \Leftrightarrow C = \text{arcsin}(\frac{12}{12,649110640674}) \approx 71,565=71^\circ 33' 54,2" \text{ (Formule sinus)}\\ -----alternatief----\\ \text{tan}(B)=\frac{4}{12} \Leftrightarrow B = \text{arctan}(\frac{4}{12})\approx 18,435=18^\circ 26' 5,8" \text{ (Formule tangens)}\\ \text{tan}(C)=\frac{12}{4} \Leftrightarrow C = \text{arctan}(\frac{12}{4})\approx 71,565=71^\circ 33' 54,2" \text{ (Formule tangens)}\\ -----controle-----\\ B + C = 90^\circ \Leftrightarrow 18^\circ 26' 5,8"+71^\circ 33' 54,2" = 90^\circ \text{(Complementaire hoeken)}\)