What is the value of sintheta for a solid angle?

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There is no "solid angle" here- two intersecting line segments lie in a single plane. Neither of the formulas you give is correct. If you drop a perpendicular from the point (x, a/2, h) to the x-axis, its length will NOT be h, it will be sqrt(a^2/4+ h^2) so the sine of the angle will be sqrt(a^2/4+ y^2)/sqrt(x^2+ a^2/4+ h^2).