document.write( "Question 257933: in a right triangle the sides a=2, and b=4, the function cos A equals? \n" ); document.write( "
Algebra.Com's Answer #189797 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
in a right triangle the sides a=2, and b=4, the function cos A equals?\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "To do that problem you must learn the parts of a right triangle. \r\n" );
document.write( "That is, you MUST learn:\r\n" );
document.write( "\r\n" );
document.write( "1. What the leg opposite a given angle means\r\n" );
document.write( "2. What the leg adjacent to a given angle means\r\n" );
document.write( "3. What the hypotenuse means\r\n" );
document.write( "\r\n" );
document.write( "The hypotenuse is the longest side of a right triangle. It is also\r\n" );
document.write( "the side opposite the right angle.  \"Opposite an angle\" means\r\n" );
document.write( "\"across the triangle from the angle\".\r\n" );
document.write( "\r\n" );
document.write( "The other two sides of a right triangle are shorter than the\r\n" );
document.write( "hypotenuse and are called \"legs\".\r\n" );
document.write( "\r\n" );
document.write( "The leg which is next to an angle is called the \"adjacent leg\"\r\n" );
document.write( "of that angle.\r\n" );
document.write( "\r\n" );
document.write( "The leg which is NOT adjacent to but is across the triangle from\r\n" );
document.write( "an angle is called the \"opposite leg\" of that angle.\r\n" );
document.write( "\r\n" );
document.write( "Observe that the side which is opposite one acute angle is\r\n" );
document.write( "adjacent to the other acute angle.\r\n" );
document.write( "\r\n" );
document.write( "Then you MUST memorize the 3 trig ratios:\r\n" );
document.write( "\r\n" );
document.write( "1. \"sin%28A%29+=+%28leg_opposite_angle_A%29%2F%28hypotenuse%29\"\r\n" );
document.write( "\r\n" );
document.write( "2. \"cos%28A%29+=+%28leg_adjacent_angle_A%29%2F%28hypotenuse%29\"\r\n" );
document.write( "\r\n" );
document.write( "3. \"tan%28A%29+=+%28leg_opposite_angle_A%29%2F%28leg_adjacent_angle_A%29\"\r\n" );
document.write( "\r\n" );
document.write( "Those three are enough for calculating purposes, but there\r\n" );
document.write( "are three other ones, the recip[rocals of the above: \r\n" );
document.write( "\r\n" );
document.write( "4. \"sec%28A%29+=+%28hypotenuse%29%2F%28leg_adjacent_angle_A%29\"\r\n" );
document.write( "\r\n" );
document.write( "5. \"csc%28A%29+=+%28hypotenuse%29%2F%28leg_opposite_angle_A%29\"\r\n" );
document.write( "\r\n" );
document.write( "6. \"cot%28A%29+=+%28leg_adjacent_angle_A%29%2F%28leg_opposite_angle_A%29\"\r\n" );
document.write( "\r\n" );
document.write( "You must also memorize the standard labeling of a right triangle\r\n" );
document.write( "ABC.\r\n" );
document.write( "\r\n" );
document.write( "1. The right angle is labeled capital \"C\".\r\n" );
document.write( "\r\n" );
document.write( "2. The leg opposite the angle A is labeled by the small letter \"a\".\r\n" );
document.write( "\r\n" );
document.write( "3. The leg opposite the angle B is labeled by the small letter \"B\".\r\n" );
document.write( "\r\n" );
document.write( "4. The hypotenuse is labeled by the small letter \"c\"\r\n" );
document.write( "\r\n" );
document.write( "Now if you have memorized all that, then you are ready to\r\n" );
document.write( "tackle this problem, but not until.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "in a right triangle the sides a=2, and b=4, the function cos A equals?\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Your triangle is like this:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "You ask yourself two questions:\r\n" );
document.write( "\r\n" );
document.write( "1. What is given? \r\n" );
document.write( "\r\n" );
document.write( "2. What am I to find?\r\n" );
document.write( "\r\n" );
document.write( "The answer to question 1 is \"the leg a, opposite angle A, and leg b,\r\n" );
document.write( "adjacent angle A\"\r\n" );
document.write( "\r\n" );
document.write( "The answer to question 2 is \"the cosine of angle A\"\r\n" );
document.write( "\r\n" );
document.write( "Now you ask yourself this question:\r\n" );
document.write( "\r\n" );
document.write( "Which of the first three trig ratios am I to find.\r\n" );
document.write( "\r\n" );
document.write( "The answer is\r\n" );
document.write( "\r\n" );
document.write( "2. \"cos%28A%29+=+%28leg_adjacent_angle_A%29%2F%28hypotenuse%29\"\r\n" );
document.write( "\r\n" );
document.write( "That amounts to\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28A%29+=+b%2Fc\"\r\n" );
document.write( "\r\n" );
document.write( "You have b given but you don't have c.  So you calculate c by using\r\n" );
document.write( "\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2=2%5E2%2B4%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2=4%2B16\"\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2=20\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=sqrt%2820%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=sqrt%284%2A5%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=2sqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "So now you can get \r\n" );
document.write( "\r\n" );
document.write( "\"cos%28A%29+=+b%2Fc\"\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28A%29+=+4%2F%282sqrt%285%29%29=2%2Fsqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "Your teacher probably wants you to\r\n" );
document.write( "rationalize the denominator and get\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28A%29+=+%282sqrt%285%29%29%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );