document.write( "Question 558984: i dont know how do 30 60 90 triangles that already have one side and also 45 45 90 triangles and sin-1 and all that please help. \n" ); document.write( "
Algebra.Com's Answer #363506 by AnlytcPhil(1806) $\"\"$ $\"About$
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document.write( "A 45°-45°-90° is found by starting with a square, like this,\r\n" );
document.write( "where all the sides are equal and all the angles equal 90°:\r\n" );
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document.write( "Then we cut it in two, with a diagonal:\r\n" );
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document.write( "That makes the angles at the upper right and lower left to be 45° \r\n" );
document.write( "each because they are half of a 90° angle, and it makes two 45° angles \r\n" );
document.write( "at the lower left and upper right:\r\n" );
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document.write( "Now we throw away the top half and keep the bottom half, like this:\r\n" );
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document.write( "That is a 45°-45°-90° right triangle.  It is half of a square. Now \r\n" );
document.write( "since the original square had all four sides equal, that means that in \r\n" );
document.write( "a 45°-45°-90° right triangle, the bottom side is exactly equal to the\r\n" );
document.write( "right side. That means that the important thing about a 45°-45°-90° right triangle is that it is an isosceles right triangle.\r\n" );
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document.write( "It is customary to say that the two equal sides are 1 unit each. Like this:\r\n" );
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document.write( "Now we need to find the length of the longest side, or hypotenuse, which is \r\n" );
document.write( "the slanted side.  To find that we'll use the Pythagorean theorem:\r\n" );
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document.write( "       a² + b² = c²\r\n" );
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document.write( "We will let \"a\" be the bottom side, 1, and \"b\" be the right side, also 1,\r\n" );
document.write( "and find \"c\", the hypotenuse. Substituting:\r\n" );
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document.write( "     (1)² + (1)² = c²\r\n" );
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document.write( "           1 + 1 = c²\r\n" );
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document.write( "               2 = c²\r\n" );
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document.write( "              Take square roots of both sides of the equation:\r\n" );
document.write( "               _\r\n" );
document.write( "              Ö2 = c\r\n" );
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document.write( "So we label the hypotenuse as Ö2\r\n" );
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document.write( "and now the 45°-45°-90° right triangle is complete, for\r\n" );
document.write( "we know all three angles and all three sides, and all\r\n" );
document.write( "three angles,\r\n" );
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document.write( "Now be sure to memorize this important triangle, its angles and its\r\n" );
document.write( "sides, because from it you can get all the trigonometric ratios for\r\n" );
document.write( "45°, which is a very important angles.  It is one of the angles known\r\n" );
document.write( "as SPECIAL angles.\r\n" );
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document.write( "Looking at the triangle above, and remembering the definitions of the\r\n" );
document.write( "sine, cosine, tangent, secant, cosecant, and cotangent, we see that\r\n" );
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document.write( "sin(45°) =  =  = \r\n" );
document.write( "cos(45°) =  =  = \r\n" );
document.write( "tan(45°) =  =  = 1\r\n" );
document.write( "sec(45°) =  =  = \r\n" );
document.write( "csc(45°) =  =  = \r\n" );
document.write( "cot(45°) =  =  = 1\r\n" );
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document.write( "Edwin
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