Question-156548

Question Number 156548 by mnjuly1970 last updated on 12/Oct/21

Commented by amin96 last updated on 12/Oct/21

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Commented by amin96 last updated on 12/Oct/21

∠A+∠C=∠B+∠D=180° ∠B=120° AC^2 =4+9−12cos(120)=9+AD^2 −6ADcos(60) 19=9+AD^2 −3AD AD^2 −3AD−10=0 AD=5

$$\angle{A}+\angle{C}=\angle{B}+\angle{D}=\mathrm{180}° \\ $$$$\angle{B}=\mathrm{120}° \\ $$$${AC}^{\mathrm{2}} =\mathrm{4}+\mathrm{9}−\mathrm{12}{cos}\left(\mathrm{120}\right)=\mathrm{9}+{AD}^{\mathrm{2}} −\mathrm{6}{ADcos}\left(\mathrm{60}\right) \\ $$$$\mathrm{19}=\mathrm{9}+{AD}^{\mathrm{2}} −\mathrm{3}{AD} \\ $$$${AD}^{\mathrm{2}} −\mathrm{3}{AD}−\mathrm{10}=\mathrm{0}\:\:\:{AD}=\mathrm{5} \\ $$

Answered by mr W last updated on 12/Oct/21