Goniometrie

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

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\( a = \sqrt{14^2+12^2} \approx 18{,}439 \text{ (Pythagoras)} \\ \text{sin}(B)=\frac{14}{18{,}439} \Leftrightarrow B = \text{arcsin}(\frac{14}{18{,}439088914586}) \approx 49{,}399=49^\circ 23' 55{,}3" \text{ (Formule sinus)}\\ \text{sin}(C)=\frac{12}{18{,}439} \Leftrightarrow C = \text{arcsin}(\frac{12}{18{,}439088914586}) \approx 40{,}601=40^\circ 36' 4{,}7" \text{ (Formule sinus)}\\ -----alternatief----\\ \text{tan}(B)=\frac{14}{12} \Leftrightarrow B = \text{arctan}(\frac{14}{12})\approx 49{,}399=49^\circ 23' 55{,}3" \text{ (Formule tangens)}\\ \text{tan}(C)=\frac{12}{14} \Leftrightarrow C = \text{arctan}(\frac{12}{14})\approx 40{,}601=40^\circ 36' 4{,}7" \text{ (Formule tangens)}\\ -----controle-----\\ B + C = 90^\circ \Leftrightarrow 49^\circ 23' 55{,}3"+40^\circ 36' 4{,}7" = 90^\circ \text{(Complementaire hoeken)}\)