Question 750137
I am given a right triangle with angle measures of 15 and 75 degrees.  The side opposite the  15 degree angle is 2 units long.  The question asks me to calculate the exact length of the hypotenuse in radical form.
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c is the hypotenuse
sin(15) = 2/c
c = 2/sin(15)
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Use the Half-Angle formula to get sin(15)
{{{sin(15) = (sqr(2 - sqr(3))/2)}}}
{{{c = 2/(sqrt(2 - sqr(3))/2)}}}
{{{c = 4/(sqrt(2 - sqr(3)))}}}
{{{c^2 = 16/(2 - sqrt(3))}}}
{{{c^2 = 16*(2 + sqrt(3))}}}
{{{c = 4sqrt(2 + sqrt(3))}}}