document.write( "Question 174528: In triangle ABC ,angle ACB is 90 degrees and CD is perpendicular to AB.Prove CB²/CA²=BD/AD \n" ); document.write( "

Algebra.Com's Answer #129556 by jojo14344(1513) $\"\"$ $\"About$

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\n" ); document.write( "In triangle ABC ,angle ACB is 90 degrees and CD is perpendicular to AB.
\n" ); document.write( ".
\n" ); document.write( "Let's draw the Triangle according to the condition:
\n" ); document.write( " -------> \" $\"CD\"$ \" perpendicular to \" $\"AB\"$ \"; Angle \" $\"ACB=90%5Eo\"$ \"
\n" ); document.write( ".
\n" ); document.write( "In Trigonometric Function for Right Triangles, $\"tan%2845%5Eo%29=1\"$ , and we know $\"tangent=opp%2Fadjacent\"$
\n" ); document.write( "And it shows in our Triangle, $\"tan%2845%5Eo%29=highlight%28AD%29%2FCD=highlight%281%29%2F1=1\"$
\n" ); document.write( "Also, $\"tan%2845%5Eo%29=highlight%28BD%29%2FCD=highlight%281%29%2F1=1\"$
\n" ); document.write( ".
\n" ); document.write( "By Pyth. Theorem: ----> $\"hyp%5E2=opp%5E2%2Badj%5E2\"$
\n" ); document.write( " $\"CA%5E2=AD%5E2%2BCD%5E2=1%5E2%2B1%5E2=1%2B1\"$
\n" ); document.write( " $\"highlight%28CA%5E2=2%29\"$
\n" ); document.write( "Also, $\"CB%5E2=CD%5E2%2BBD%5E2=1%5E2%2B1%5E2=1%2B1\"$
\n" ); document.write( " $\"highlight%28CB%5E2=2%29\"$
\n" ); document.write( "Therefore,
\n" ); document.write( "Prove $\"CB%5E2%2FCA%5E2=BD%2FAD\"$ , substitute highlighted values:
\n" ); document.write( " $\"2%2F2=1%2F1\"$
\n" ); document.write( " $\"1=1\"$
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo \n" ); document.write( "

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