document.write( "Question 1159001: Recall that the lengths of the sides of triangle ABC are often abbreviated by writing a = BC, b = CA, and c = AB. Sketch triangle ABC where angle BCA is right and mark F as the foot of the perpendicular drawn from C to the hypotenuse AB. In terms of a, b, and c, express the lengths of FA, FB, and FC. The equation c = FA+FB can be used to check your work. \n" ); document.write( "
Algebra.Com's Answer #854603 by KMST(5396)\"\" \"About 
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This is our first triangle: triangle ABC
\n" ); document.write( "When I draw the perpendicular from C to hypotenuse AB, we will have point F, and the first triangle will be split into 2 triangles.
\n" ); document.write( "I will labeled them as triangle #2 and triangle #3.
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\n" ); document.write( "Triangle ABC, triangle #2, and triangle #3 are similar triangles. They have the same shape, the same angle measures, and the same ratios of corresponding sides.
\n" ); document.write( "For the ratio of side opposite \"alpha\" to hypotenuse we have:
\n" ); document.write( "\"b%2Fc=FC%2Fa=FA%2Fb\" --> \"system%28highlight%28FC=ab%2Fc%29%2Chighlight%28FA=b%5E2%2Fc%29%29\"
\n" ); document.write( "For the ratio of side opposite \"beta\" to hypotenuse we have:
\n" ); document.write( "\"a%2Fc=FB%2Fa=FC%2Fb\" --> \"system%28highlight%28FB=a%5E2%2Fc%29%2CFC=ab%2Fc%29\"
\n" ); document.write( "Of course, we know that \"FA%2BFB=BC=c\" ,
\n" ); document.write( "We can verify that the expressions we found for \"FA\" and \"FB\" are correct, by substituting, and finding that it agrees with what we know:
\n" ); document.write( "From \"c=FA%2BFB\" --> \"c=b%5E2%2Fc%2Ba%5E2%2Fc\" --> \"c=%28b%5E2%2Ba%5E2%29%2Fc\" --> \"c%5E2=b%5E2%2Ba%5E2\" .
\n" ); document.write( "However, along the way, we find that we proved the Pythagorean theorem from our knowledge about similar triangles.
\n" ); document.write( "We can also prove that \"FC%5E2=FA%2AFC\" <--> \"FC=sqrt%28FA%2AFC%29\" . \n" ); document.write( "
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