Question Number 168643 by BagusSetyoWibowo last updated on 15/Apr/22
Commented by som(math1967) last updated on 15/Apr/22
$$\boldsymbol{{x}}.\boldsymbol{{y}}=\mathrm{10}\:\boldsymbol{{if}}\:\:\boldsymbol{{triangle}}\:\boldsymbol{{is}}\:\boldsymbol{{rt}}.\boldsymbol{{angle}} \\ $$
Commented by safojontoshtemirov last updated on 15/Apr/22
$$\frac{{y}}{\mathrm{5}}=\frac{{x}}{\mathrm{8}\:\:}\:\:\:{x}=\frac{\mathrm{8}{y}}{\mathrm{5}} \\ $$$${x}^{\mathrm{2}} +\left({m}+{n}\right)^{\mathrm{2}} =\mathrm{64} \\ $$$$\frac{{m}+{n}}{\mathrm{8}}={cos}\mathrm{30}°\:\:\:\:{m}+{n}=\mathrm{4}\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{2}} +\mathrm{48}=\mathrm{64}\:\:\:\:{x}=\mathrm{4}\:\:\:\:\mathrm{4}=\frac{\mathrm{8}{y}}{\mathrm{5}}\:\:\:{y}=\mathrm{2}.\mathrm{5} \\ $$$${xy}=\mathrm{4}\centerdot\mathrm{2}.\mathrm{5}=\mathrm{10} \\ $$$$ \\ $$
Commented by mr W last updated on 15/Apr/22
$$\mathrm{sin}\:\mathrm{30}°=\mathrm{0}.\mathrm{5} \\ $$$${y}=\mathrm{5}\:\mathrm{sin}\:\mathrm{30}°=\mathrm{2}.\mathrm{5} \\ $$$${x}=\left(\mathrm{5}+\mathrm{3}\right)\:\mathrm{sin}\:\mathrm{30}°=\mathrm{4} \\ $$$${xy}=\mathrm{4}×\mathrm{2}.\mathrm{5}=\mathrm{10} \\ $$