document.write( "Question 86994:
\r\n" ); document.write( "Please help me solve this problem: the vertex \r\n" ); document.write( "angle of an isosceles triangle is 57°24' \r\n" ); document.write( "and each of its equal sides is 375.5 ft. long.\r\n" ); document.write( "Find the altitude of the \r\n" ); document.write( "triangle.
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Algebra.Com's Answer #62953 by Edwin McCravy(20063) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Please help me solve this problem: the vertex \r\n" );
document.write( "angle of an isosceles triangle is 57°24' \r\n" );
document.write( "and each of its equal sides is  375.5 ft. long.\r\n" );
document.write( "Find the altitude of the \r\n" );
document.write( "triangle.\r\n" );
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document.write( "The solution by Stanbon contains an error in\r\n" );
document.write( "calculation. He did it a different way, i.e.,\r\n" );
document.write( "by calculating the base angles, but he calculated \r\n" );
document.write( "the base angles as 62°18' and they should have \r\n" );
document.write( "been 61°18'. \r\n" );
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document.write( "A triangle has three altitudes.  I assume you \r\n" );
document.write( "mean the altitude from the vertex angle to the \r\n" );
document.write( "base. \r\n" );
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document.write( "Now draw in the altitude (call it \"a\") from the \r\n" );
document.write( "vertex angle to the base.\r\n" );
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document.write( " The altitude divides the triangle into two \r\n" );
document.write( "congruent right triangles, and divides the vertex \r\n" );
document.write( "angle by 2.  So each angle at the top is one-half of \r\n" );
document.write( "57°24'. Since 57° is an odd number, and doesn't divide\r\n" );
document.write( "evenly by 2, borrow one degree from the 57°, \r\n" );
document.write( "making it an even number 56°, change the borrowed degree \r\n" );
document.write( "to 60' and add it to the 24', giving 56°84':\r\n" );
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document.write( "57°48 ÷ 2 = 56°84' ÷ 2 = 28°42' \r\n" );
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document.write( "Now let's erase the right triangle on the right side \r\n" );
document.write( "and just look at the one on the left:\r\n" );
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document.write( "The altitude \"a\" is the side adjacent to the 28°42' angle.\r\n" );
document.write( "The side which is 375.5 feet is the hypotenuse.  So you\r\n" );
document.write( "need the basic trig function that involves adjacent and\r\n" );
document.write( "hypotenuse, which is the cosine, so we have\r\n" );
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document.write( "cos(28°42') = \r\n" );
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document.write( "cos(28°42') = \r\n" );
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document.write( "Multiply both sides by 375.5\r\n" );
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document.write( "(375.5)cos(28°42') = a\r\n" );
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document.write( "The easiest way to handle 28°42' is to put the minutes\r\n" );
document.write( "over 60 and add that to the number of degrees, that is, \r\n" );
document.write( "enter\r\n" );
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document.write( "375.5 × cos(28 + 42/60)\r\n" );
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document.write( "on your calculator to get\r\n" );
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document.write( "a = 329.3683845.  You should round\r\n" );
document.write( "that to tenths since the given side\r\n" );
document.write( "was rounded to tenths.  So the\r\n" );
document.write( "altitude from the vertex angle to the \r\n" );
document.write( "base in the original isosceles triangle\r\n" );
document.write( "is: \r\n" );
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document.write( "a = 329.4 ft.\r\n" );
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document.write( "Edwin

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