If `a=9,b=4a n dc=8` then find the distance between the middle point of BC and the foot of the perpendicular form `Adot`

Explanation

Let D be the middle point of BC and AE be the perpendicular on BC from A
`DE = CD - CE`
`= (a)/(2) - b cos C`
`= (a)/(2) - b (a^(2) + b^(2) - c^(2))/(2ab)`
`= (c^(2) - b^(2))/(2a)`
`= (64 - 16)/(18) = (8)/(3)`