Question Number 147706 by aliibrahim1 last updated on 22/Jul/21
Answered by mr W last updated on 22/Jul/21
Commented by aliibrahim1 last updated on 22/Jul/21
$${sorry}\:{sir}\:{i}\:{tried}\:{to}\:{build}\:{on}\:{that}\:{before}\:{sending}\:{it}\:{didnt}\:{work}\:{with}\:{me} \\ $$
Commented by mr W last updated on 22/Jul/21
$${say}\:{A}\left({p},{p}^{\mathrm{2}} \right) \\ $$$${s}=\mathrm{2}{p} \\ $$$$\beta=\frac{\mathrm{180}−\mathrm{108}}{\mathrm{2}}=\mathrm{36}° \\ $$$$\alpha=\mathrm{108}−\mathrm{36}=\mathrm{72}° \\ $$$${x}_{{B}} ={p}+\mathrm{2}{p}\:\mathrm{cos}\:\mathrm{72}° \\ $$$${y}_{{B}} ={p}^{\mathrm{2}} +\mathrm{2}{p}\:\mathrm{sin}\:\mathrm{72}° \\ $$$${p}^{\mathrm{2}} +\mathrm{2}{p}\:\mathrm{sin}\:\mathrm{72}°={p}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{2}\:\mathrm{cos}\:\mathrm{72}°\right)^{\mathrm{2}} \\ $$$$\mathrm{sin}\:\mathrm{72}°=\mathrm{2}{p}\mathrm{cos}\:\mathrm{72}°\left(\mathrm{1}+\mathrm{cos}\:\mathrm{72}°\right) \\ $$$${p}=\frac{\mathrm{tan}\:\mathrm{72}°}{\mathrm{2}\left(\mathrm{1}+\mathrm{cos}\:\mathrm{72}°\right)} \\ $$$${y}_{{C}} ={y}_{{B}} +\mathrm{2}{p}\:\mathrm{sin}\:\mathrm{36}° \\ $$$${y}_{{C}} ={p}^{\mathrm{2}} +\mathrm{2}{p}\left(\mathrm{sin}\:\mathrm{72}°+\mathrm{sin}\:\mathrm{36}°\right) \\ $$$${y}_{{C}} =\frac{\mathrm{tan}^{\mathrm{2}} \:\mathrm{72}°}{\mathrm{4}\left(\mathrm{1}+\mathrm{cos}\:\mathrm{72}°\right)^{\mathrm{2}} }+\frac{\mathrm{tan}\:\mathrm{72}°}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{72}°\right)}\left(\mathrm{sin}\:\mathrm{72}°+\mathrm{sin}\:\mathrm{36}°\right) \\ $$$$=\mathrm{5} \\ $$
Commented by aliibrahim1 last updated on 23/Jul/21
$${thanks}\:{sir}\:{appreciate}\:{it} \\ $$