# Relationship between two planes - calculating an angle

#### jonesy118

##### New member
I'd like some help on the following... I know the answer for the case below, having drawn it in CAD, however I'd like to understand the methodology as to how I can calculate this manually, given some known dimensions/angles.

3000x3000 square base, with two intersecting 25 degree planes. Diagonal between bottom left corner and top right corner appears as being 45 degree, when the 3D shape is viewed in plan.

How do I arrive at the angle of 42.186 degree?, given that the values above and the attached drawing. I assume a triangle/series of triangles will get me there, but I'm stumped

#### tkhunny

##### Moderator
Staff member
It's not clear to me which angle you are measuring?

Frankly, if the line on the left of the marked angle is parallel to the axis extending to the left, why wouldn't it be 45º? Unless we're not talking about the same plane?

#### jonesy118

##### New member
It's not clear to me which angle you are measuring?

Frankly, if the line on the left of the marked angle is parallel to the axis extending to the left, why wouldn't it be 45º? Unless we're not talking about the same plane?
This was probably too simple an example in all honesty, because it's using equal pitches and both of the slopes are right triangles, so is very easy to approach.

The angle isn't 45 deg because the plane spans 3000 at 25 degrees upto the rear-right point, so the hypotenuse of the triangle formed by the green dashed line is 3310

Therefore the triangle for the plane in question has sides of 3000, 3310 and the hypotenuse where the two planes intersect is 4467, resulting in the angles. I will try and draw up a more complex case, as it must be possible to generalise.

As background, this is to calculate side cutting angles for jack rafters in roofing projects

#### Dr.Peterson

##### Elite Member
I'd like some help on the following... I know the answer for the case below, having drawn it in CAD, however I'd like to understand the methodology as to how I can calculate this manually, given some known dimensions/angles.

3000x3000 square base, with two intersecting 25 degree planes. Diagonal between bottom left corner and top right corner appears as being 45 degree, when the 3D shape is viewed in plan.

How do I arrive at the angle of 42.186 degree?, given that the values above and the attached drawing. I assume a triangle/series of triangles will get me there, but I'm stumped

View attachment 9093
I think the marked angle is the same as the angle at the apex (on the vertical axis) on the shaded triangle. To find it, find the length of the segment from the apex down to the left to the axis, using the Pythagorean theorem (or a cosine). Then you know the legs of the shaded right triangle, and can find the angle at the apex. I get the stated value this way.