Answer: 9/41
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Explanation:
We have a triangle with these three sides.
Use the pythagorean theorem to find b
a^2+b^2 = c^2
b = sqrt(c^2 - a^2)
b = sqrt(82^2 - 80^2)
b = sqrt(324)
b = 18
This is the missing vertical leg of the triangle. And this is also the side opposite angle C.
We have enough information to compute the sine of the angle.
sin(angle) = opposite/hypotenuse
sin(C) = AB/AC
sin(C) = 18/82
sin(C) = (9*2)/(41*2)
sin(C) = 9/41
