document.write( "Question 1197389: What are the side lengths of the right triangles of 45-45-90 and 30-60-90? \n" ); document.write( "

Algebra.Com's Answer #830634 by math_helper(2461) $\"\"$ $\"About$

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document.write( "There is no fixed length for either of these triangles.  Rather, there is a RELATIONSHIP between the hypotenuse and shorter two sides.  For example, for a 45-45-90 triangle, the two shorter legs have equal length, and we can call this length L.  If we do this, the hypotenuse h has length  .\r
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document.write( "This follows from the Pythagorean Theorem  where for any right triangle, the hypotenuse is related to the other two sides, a and b, by:  
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document.write( "Back to the 45-45-90 triangle:  
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document.write( "So, if I pick L=10cm, h will be about 14.14cm
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document.write( "I can also pick L=23m, and h will then be 32.53m,  etc.
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document.write( "The important thing to note is both of these examples give you a 45-45-90 triangle.\r
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document.write( "For the 30-60-90 triangle,  h is as before (square root of sum of squares of shorter two sides) but the relation of h to the shorter two sides is as follows:\r
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document.write( "   a = h * sin(30) = 
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document.write( "   b = h * cos(30) = \r
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document.write( "where  a is the side opposite the 30 degree angle, and b is the side adjacent to the 30 degree angle (such that the 30 degree angle comes between 'b' and 'h').\r
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document.write( "Notice for the 30-60-90 triangle, the Pythagorean Theorem still holds, as it does for all right triangles:
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document.write( "      h =   
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document.write( "        = 
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document.write( "        = 
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document.write( "        =     \r
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document.write( "Hope this helps!
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