document.write( "Question 40414This question is from textbook 15 Realistic Tests for the SAT Math Level 2 Subject Test
\n" ); document.write( ": i-ABC is an acute triangle
\n" ); document.write( "ii-ABC is an isosceles traingle
\n" ); document.write( "iii-ABC is an obtuse triangle where B is an obtuse angle
\n" ); document.write( "iv-ABC is a right triangle where A is the right angle
\n" ); document.write( "v-ABC is an obtuse triagnle where A is the obtuse angle
\n" ); document.write( "In a triangle ABC, sinA < a/c and cosA > b/c. How many of the above statements are always false regarding triangle ABC?
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\n" ); document.write( "why?
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Algebra.Com's Answer #25789 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
i- ABC is an acute triangle
\n" ); document.write( " ii- ABC is an isosceles traingle
\n" ); document.write( "iii- ABC is an obtuse triangle where B is an obtuse angle
\n" ); document.write( " iv- ABC is a right triangle where A is the right angle
\n" ); document.write( " v- ABC is an obtuse triagnle where A is the obtuse angle
\n" ); document.write( " vi- In triangle ABC, sinA < a/c and cosA > b/c. \r
\n" ); document.write( "\n" ); document.write( "How many of the above statements are always false regarding triangle ABC?
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document.write( "iii, iv, v are NEVER true.\r\n" );
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document.write( "Here's why:\r\n" );
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document.write( "Draw the figure:\r\n" );
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document.write( "       B  \r\n" );
document.write( "      /|\r\n" );
document.write( "     / |\r\n" );
document.write( "  c /  |a\r\n" );
document.write( "   /   |\r\n" );
document.write( "  /   _|\r\n" );
document.write( "A/___|_|C\r\n" );
document.write( "    b\r\n" );
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document.write( "i-ABC is an acute triangle\r\n" );
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document.write( "Yes this is always true because C is a 90° angle,\r\n" );
document.write( "and the sum of all three angles of a triangle is\r\n" );
document.write( "180°, so the sum of A and B must equal 90°. So each\r\n" );
document.write( "of the other angles must be less than 90°. \r\n" );
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document.write( "ii-ABC is an isosceles traingle\r\n" );
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document.write( "This is sometimes the case when a and b are equal and\r\n" );
document.write( "A and B are both 45°.\r\n" );
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document.write( "iii-ABC is an obtuse triangle where B is an obtuse angle\r\n" );
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document.write( "This is NEVER the case because C is a 90° angle,\r\n" );
document.write( "and the sum of all three angles of a triangle is\r\n" );
document.write( "180°, but an obtuse angle is greater than 90°, so\r\n" );
document.write( "if B were an obtuse angle, that would make the \r\n" );
document.write( "sum more than 180°.\r\n" );
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document.write( "iv-ABC is a right triangle where A is the right angle\r\n" );
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document.write( "This is NEVER the case because C is a 90° angle,\r\n" );
document.write( "and the sum of all three angles of a triangle is\r\n" );
document.write( "180°, and if A were 90°, that would make the sum\r\n" );
document.write( "of A and C 180°, leaving 0° for B to equal, but\r\n" );
document.write( "no triangle can have a 0° angle.\r\n" );
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document.write( "v-ABC is an obtuse triagnle where A is the obtuse angle\r\n" );
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document.write( "This is NEVER the case because C is a 90° angle,\r\n" );
document.write( "and the sum of all three angles of a triangle is\r\n" );
document.write( "180°, but an obtuse angle is greater than 90°, so\r\n" );
document.write( "if A were an obtuse angle, that  would make the \r\n" );
document.write( "sum more than 180°.\r\n" );
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document.write( "vi- In triangle ABC, sinA < a/c and cosA > b/c.\r\n" );
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document.write( "If you use the convention where side a is opposite\r\n" );
document.write( "angle A, side b is opposite angle B, and side c is\r\n" );
document.write( "the hypotenuse, then this is NEVER the case because\r\n" );
document.write( "sinA = a/c and cosA = b/c, never > or < .\r\n" );
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document.write( "However, if you vary from this notation, and have\r\n" );
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document.write( "       A  \r\n" );
document.write( "      /|\r\n" );
document.write( "     / |\r\n" );
document.write( "  c /  |a\r\n" );
document.write( "   /   |\r\n" );
document.write( "  /   _|\r\n" );
document.write( "B/___|_|C\r\n" );
document.write( "    b\r\n" );
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document.write( "then sinA < a/c and cosA > a/c\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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