Question 1022160: in Pythagorean theorem how can you derive you're answer to 1.414 in 45 degree
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this depends on what you're given.
the sine of an angle is equal to the length of the side opposite divided by the hypotenuse.
the cosine of an angle is equal to the length of the side adjacent divided by the hypotenuse.
in a 45 degree triangle, both the sine and the cosine of the angle are the same.
if you are dealing with a right triangle, and one of the acute angles is 45 degrees, then the other acute angle has to be 45 degrees as well because the sum of the acute angles of a right triangle has to be equal to 90 degrees.
since the angles are equal, then the sides opposite these angles have to be equal as well.
let's assume that the length of each side is x.
the hypotenuse of a right triangle, by the pythagorean formula, is equal to the square root of the sum of the square of the legs.
this means that the hypotenuse is equal to the square root of (x^2 + x^2).
this means that the hypotenuse is equal to the square root of (2x^2).
this means that the hypotenuse is equal to the square root of (2) * the square root of (x^2).
since the square root of x^2 is equal to x, this means that the hypotenuse is equal to the square root of (2) * x.
since the square root of (2) is equal to 1.414....., this means that the hypotenuse is equal to 1.414.... * x.
if x is equal to 1, then the hypotenuse becomes equal to 1.414 ....., because 1.414... * 1 is equal to 1.414...
that's where it comes from.
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