document.write( "Question 1041081: Use the following ratios to address the questions below:
\n" ); document.write( "a. sin = 1/2
\n" ); document.write( "b. sin = 6/13
\n" ); document.write( "c. sin = 9/10
\n" ); document.write( "d. sin = 12/15
\n" ); document.write( "e. cos = 1/2
\n" ); document.write( "f. cos = 6/13
\n" ); document.write( "g. cos = 9/10
\n" ); document.write( "h. cos = 12/15
\n" ); document.write( "i. tan = 1/2
\n" ); document.write( "j. tan = 6/13
\n" ); document.write( "k. tan = 9/10
\n" ); document.write( "l. tan = 12/15 \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1. Use each trigonometric ratio to determine the length of all three sides of each triangle. Did you notice a pattern in the answers? If so, make sure you can explain the pattern. \r
\n" ); document.write( "\n" ); document.write( "2. Using similar triangles, calculate the altitude of each triangle. Round your answers to the nearest hundredth, if necessary.
\n" ); document.write( "Also, how do you calculate the sine, cosine, and tangent of any angle between 0 and 90 using a calculator or other technology? \r
\n" ); document.write( "\n" ); document.write( "Thanks in advance! \n" ); document.write( "
Algebra.Com's Answer #656027 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Use the facts:\r\n" );
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document.write( "\"SINE=OPPOSITE%2FHYPOTENUSE\"\r\n" );
document.write( "\"COSINE=ADJACENT%2FHYPOTENUSE\"\r\n" );
document.write( "\"TANGENT=OPPOSITE%2FADJACENT\"\r\n" );
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document.write( "to make this chart\r\n" );
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document.write( "                  opposite     adjacent    hypotenuse  \r\n" );
document.write( "a. sin = 1/2          1                        2\r\n" );
document.write( "b. sin = 6/13         6                       13\r\n" );
document.write( "c. sin = 9/10         9                       10\r\n" );
document.write( "d. sin = 12/15       12                       15\r\n" );
document.write( "e. cos = 1/2                      1            2\r\n" );
document.write( "f. cos = 6/13                     6           13\r\n" );
document.write( "g. cos = 9/10                     9           10\r\n" );
document.write( "h. cos = 12/15                   12           15\r\n" );
document.write( "i. tan = 1/2          1           2\r\n" );
document.write( "j. tan = 6/13         6          13\r\n" );
document.write( "k. tan = 9/10         9          10\r\n" );
document.write( "l. tan = 12/15       12          15  \r\n" );
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document.write( "Then use the Pythagorean theorem to fill in the missing \r\n" );
document.write( "values for the missing side of the right triangle:\r\n" );
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document.write( "                  opposite     adjacent    hypotenuse  \r\n" );
document.write( "a. sin = 1/2          1          √3            2\r\n" );
document.write( "b. sin = 6/13         6          √133         13\r\n" );
document.write( "c. sin = 9/10         9          √19          10\r\n" );
document.write( "d. sin = 12/15       12          √81 = 9      15\r\n" );
document.write( "e. cos = 1/2        √3            1            2\r\n" );
document.write( "f. cos = 6/13       √133          6           13\r\n" );
document.write( "g. cos = 9/10       √19           9           10\r\n" );
document.write( "h. cos = 12/15      √81 = 9      12           15\r\n" );
document.write( "i. tan = 1/2          1           2          √5\r\n" );
document.write( "j. tan = 6/13         6          13          √205\r\n" );
document.write( "k. tan = 9/10         9          10          √181\r\n" );
document.write( "l. tan = 12/15       12          15          √369 = √(9*41) = 3√41 \r\n" );
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document.write( "The only pattern we can see so far is that the first four opposite \r\n" );
document.write( "sides are the same as the next four adjacent sides and vice-versa.\r\n" );
document.write( "Also the first four hypotenuses are the same as the next four hypotenuses.\r\n" );
document.write( "The last four have the same opposite sides as the first four, and the \r\n" );
document.write( "adjacents are the same as the hypotenuses in the first four.  So let's get \r\n" );
document.write( "a calculator and round them off to the nearest hundredth and see if we can \r\n" );
document.write( "see any other patterns:\r\n" );
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document.write( "                  opposite     adjacent    hypotenuse  \r\n" );
document.write( "a. sin = 1/2          1           1.73          2\r\n" );
document.write( "b. sin = 6/13         6          11.53         13\r\n" );
document.write( "c. sin = 9/10         9           4.36         10\r\n" );
document.write( "d. sin = 12/15       12           9.00         15\r\n" );
document.write( "e. cos = 1/2        1.73          1            2\r\n" );
document.write( "f. cos = 6/13      11.53          6           13\r\n" );
document.write( "g. cos = 9/10       4.36          9           10\r\n" );
document.write( "h. cos = 12/15      9.00         12           15\r\n" );
document.write( "i. tan = 1/2        1             2            2.24\r\n" );
document.write( "j. tan = 6/13       6            13           14.32\r\n" );
document.write( "k. tan = 9/10       9            10           13.45\r\n" );
document.write( "l. tan = 12/15     12            15           19.21\r\n" );
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document.write( "There is no other pattern except those same ones.\r\n" );
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\n" ); document.write( "2. Using similar triangles, calculate the altitude of
\n" ); document.write( "each triangle. Round your answers to the nearest hundredth,
\n" ); document.write( "if necessary.
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\r\n" );
document.write( "Since they are all right triangles their altitudes are\r\n" );
document.write( "the same as their opposite sides.  No need for similar\r\n" );
document.write( "triangles.\r\n" );
document.write( "

\n" ); document.write( "Also, how do you calculate the sine, cosine, and tangent
\n" ); document.write( "of any angle between 0 and 90 using a calculator or other
\n" ); document.write( "technology?
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\r\n" );
document.write( "On a calculator to find the sine, you put the opposite side in\r\n" );
document.write( "the calculator, press the division key, then put in the\r\n" );
document.write( "hypotenuse and press the = or enter key.\r\n" );
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document.write( "On a calculator to find the cosine, you put the adjacent side in\r\n" );
document.write( "the calculator, press the division key, then put in the\r\n" );
document.write( "hypotenuse and press the = or enter key.\r\n" );
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document.write( "On a calculator to find the tangent, you put the opposite side in\r\n" );
document.write( "the calculator, press the division key, then put in the\r\n" );
document.write( "adjacent and press the = or enter key.\r\n" );
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document.write( "[In my opinion, this is a silly problem!]\r\n" );
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document.write( "Edwin
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