MATLAB: Angle between a plane and horizontal

Question

I need to find the angle between a set of planes ax+by+cz+d = 0 and horizontal plane (x-y plane).

For example my first plane equation is x – 4y +3z +1 = 0 so i wrote the following code

n1 = [1 -4 3]; % Normal vector to plane

n2= [0 0 1]; % normal vector to x-y plane

cosang = dot(n1,n2); % actually n1.n2 = |n1||n2|cosang

n1crossn2 = cross(n1,n2);

sinang = norm(n1crossn2); % actually n1*n2 = |n1||n2|sinang n

angle = atand(sinang, cosang);

it gives an answer 53.96

I thought the angle between plane and horizontal is same as the angle between normal to both plane. Is it true? I don't know how to verify this? Also how can i check the sign of the angle(possitive or negative)?

Is there any other way to get the angle between given plane and horizontal plane? Note: I don't know the coordinates of any plane lying on that plane. I only know the plane equation

Answer 1

The angle between the two planes are the angle between the two normal vectors, so your approach is correct. I'm not sure why you need to do atand though. I think once you do the dot product, you can use acosd directily