Question

Angle B = 90 in triangle ABC. BM is altitude to AC. AB = 10 and AM = 2.5. Find MC

Answer 1

MC =37.5

Explanation:

In
`\triangle ABC,\: \angle B = 90\degree` and
`BM \perp AC.`

`\therefore \angle AMB = 90\degree`

By Pythagoras Theorem:

`AM^2 + BM^2 = AB^2 \\</p><p>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 * MC \\ 93.75 = 2.5* MC \\MC = (93.75)/(2.5) \\ \huge \orange{ \boxed{ MC =37.5}} \\`