Answer:
MC =37.5
Step-by-step explanation:
In [tex] \triangle ABC,\: \angle B = 90\degree [/tex] and [tex] BM \perp AC.[/tex]
[tex] \therefore \angle AMB = 90\degree [/tex]
By Pythagoras Theorem:
[tex]AM^2 + BM^2 = AB^2 \\
BM^2 = AB^2 - AM^2 \\ BM^2 = {10}^{2} - {2.5}^{2} \\ BM^2 = 100 -6.25 \\ \red{BM^2 = 93.75} \\ now \: by \: geometric \: mean \: theorem : \\ BM^2 =AM \times MC \\ 93.75 = 2.5\times MC \\MC = \frac{93.75}{2.5} \\ \huge \orange{ \boxed{ MC =37.5}} \\ [/tex]
