Remark that the triangle AMC is right. Therefore [tex]10^2=4^2+AM^2\text{ Pythagorian formula}[/tex] Solving the above equation for AM we get [tex]AM=9.2[/tex] Since [tex] \frac{AM}{BM}=\frac{2}{5}\text{ then }BM=\frac{5}{2}AM=\frac{5}{2}\times9.2=23 [/tex] Conclusion: [tex]AB=AM+BM=9.2+23=32[/tex] We use the Pythagorian formula on the right angles triangle MBC like this: [tex]BC^2=4^2+23^2\text{ then }BC=23.3[/tex]
