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denis23 [38]
3 years ago
9

If AD=6 and AB=24, find AC

Mathematics
1 answer:
ruslelena [56]3 years ago
6 0
When a perpendicular is dropped from the right-angle (C) to the opposite side AB, the metric relations apply:
BD*BA=a^2 ..........................(1)
AD*AB=b^2...........................(2)
BD*DA=DC^2........................(3)

Given AD=6, AB=24, using metric relation (2) above, we have
b^2=6*24=144
=>
b=sqrt(144)=12

By the way, we conclude that this is a 30-60-90 triangle because b/AB=(1/2)=sin(B) => B=30 degrees.

Answer: b=12
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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B3%20%2B%2011i%7D%20" id="TexFormula1" title=" \frac{6}{3 + 11i} " alt=" \f
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