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Question Number 184370 by cherokeesay last updated on 05/Jan/23

Commented by cherokeesay last updated on 05/Jan/23

on demande la mesure de alpha :

Answered by som(math1967) last updated on 05/Jan/23

$$\frac{AD}{DC}=\frac{sin\alpha }{sin50}$$$$\frac{AD}{AB}=\frac{sin40}{sin(50+\alpha )}$$$$\Rightarrow \frac{sin\alpha }{sin50}=\frac{sin40}{sin(50+\alpha )}$$$$\Rightarrow 2sin\alpha sin(50+\alpha )=2sin40sin50$$$$\Rightarrow cos50-cos(50+2\alpha )=cos10-cos90$$$$\Rightarrow cos(50+\alpha )=cos50-cos10$$$$\Rightarrow cos(50+\alpha )=-sin20$$$$\Rightarrow cos(50+2\alpha )=-cos70$$$$\Rightarrow cos(50+2\alpha )=cos(180-70)$$$$50+2\alpha =110$$$$\alpha =30$$

Commented by cherokeesay last updated on 05/Jan/23

$$thankyousir!$$

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