Math  /  Trigonometry

QuestionThe law of sines The law of sines says that if a,ba, b, and cc are the sides opposite the angles A,BA, B, and CC in a triangle, then sinAa=sinBb=sinCc.\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} .
Use the accompanying figures and the identity sin(πθ)=\sin (\pi-\theta)= sinθ\sin \theta, if required, to derive the law.

Studdy Solution
ساوي بين التعبيرين للارتفاع hh:
bsinA=csinB b \cdot \sin A = c \cdot \sin B
قسّم كلا الطرفين على bcbc:
sinAa=sinBb \frac{\sin A}{a} = \frac{\sin B}{b}
استخدم نفس الطريقة للزاوية CC للحصول على:
sinBb=sinCc \frac{\sin B}{b} = \frac{\sin C}{c}
وبالتالي، قانون الجيوب هو:
sinAa=sinBb=sinCc \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

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