document.write( "Question 723234: What type of triangle does 11,10 and 13 make \n" ); document.write( "

Algebra.Com's Answer #443177 by KMST(5328) $\"\"$ $\"About$

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To begin with, I would call that triangle $\"highlight%28scalene%29\"$ , meaning that the 3 sides have different lengths.
\n" ); document.write( "The triangle is also $\"highlight%28acute%29\"$ , meaning that all three angles are acute (smaller than a right angle).
\n" ); document.write( "
\n" ); document.write( "How do I know? Here is how.
\n" ); document.write( "The largest angle is opposite the longest side, the one measuring 13.
\n" ); document.write( "(for triangles, longer side is opposite larger angle, and shorter side is opposite smaller angle.
\n" ); document.write( "According to the Pythagorean theorem, a right triangle with legs (the shorter sides) measuring 10 and 11 would have a hypotenuse (the longer side) measuring
\n" ); document.write( " $\"sqrt%2810%5E2%2B11%5E2%29=sqrt%28100%2B121%29=sqrt%28221%29\"$ =about 14.87
\n" ); document.write( "and would look like this

\n" ); document.write( "If side AB has a shorter measure, $\"13%3Csqrt%28221%29\"$ , then angle C must be smaller than a right angle.
\n" ); document.write( "And since A is the largest of the 3 angles, all three angles are smaller than a right angle:
\n" ); document.write( "

I can calculate the angle measures as $\"A=48.4%5Eo\"$ , $\"B=55.3%5Eo\"$ , and $\"C=76.3%5Eo\"$ using the law of cosines, but that is much more advanced math (and not a fun calculation either). \n" ); document.write( "

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