# Calculate Slope of a Triangle for Vertex Alpha

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Given 3 points of a triangle in CCW orientation, how can I calculate its angle based off flat xz plane. I need to find the so called "slope" of triangles on the terrain so I can calculate vertex alpha's

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So you just need to know what angle the triangle is 'tilted' at in relation to the xz plane? The normal to the xz plane is [0 1 0]. Dot this with the (unit-length) triangle normal [nx ny nz], and you get ny. This is the cosine of the angle between the triangle normal and the 'up' vector. What you end up with is simply:

angle = acos(clamp(triangle.normal.y, -1, 1));

The greater the angle, the steeper the slope (a horizontal triangle will have an angle of 0, a vertical triangle will have an angle of pi/2).

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