Levi Rizki Saputra Notes

Hukum Sinus

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Ilustrasi hukum sinus

sinA=dbd=bsinAsinB=dad=asinBsinAa=sinBb\begin{align*} \sin\angle A & =\frac{d}{b}\\ d & =b\sin\angle A\\ \sin\angle B & =\frac{d}{a}\\ d & =a\sin\angle B\\ \frac{\sin\angle A}{a} & =\frac{\sin\angle B}{b} \end{align*}

Jika diturunkan lagi ditemukan:

sinAa=sinBb=sinCc\frac{\sin\angle A}{a}=\frac{\sin\angle B}{b}=\frac{\sin\angle C}{c}

Bisa juga ditulis

1(sinAa)=1(sinBb)=1(sinCc)asinA=bsinB=csinC\begin{alignat*}{3} \frac{1}{\left(\frac{\sin\angle A}{a}\right)} & = & \frac{1}{\left(\frac{\sin\angle B}{b}\right)} & = & \frac{1}{\left(\frac{\sin\angle C}{c}\right)}\\ \frac{a}{\sin\angle A} & = & \frac{b}{\sin\angle B} & = & \frac{c}{\sin\angle C} \end{alignat*}