SOLUTION: The lengths of the sides of triangle ABC are often abbreviated by writing a = BC, b = CA, and c = AB. Notice that lower-case sides oppose upper-case vertices. Suppose now that angl

Question 1154274: The lengths of the sides of triangle ABC are often abbreviated by writing a = BC, b = CA, and c = AB. Notice that lower-case sides oppose upper-case vertices. Suppose now that angle BCA is right, so that a2 + b2 = c2. Let F be the foot of the perpendicular drawn fromCtothehypotenuseAB. Ifa=5,b=12andc=13,whatarethelengthsofFA, FB,andFC? Doesc=FA+FB?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

Triangle ACF ~ triangle ABC
AC/AB =AF/AC
12/13 = AF/12
AF =11.08
In BCF and BAC
BC/AB = BF/BC
Plug values to get BF = 1.92
CF^2 = BF * AF ( geometric mean property)
Plug values to get CF = 4.61

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