Marking the Knee Joints - trigonometry is useful, after all

In this post, I want to go into a bit more technical detail and share how I used my GeoGebra diagram to accurately mark the knee joints for Frame B—specifically, the one located at point D in the drawing from my earlier post.

Frame D - Point D

The starting point is the angle at point D, which the GeoGebra diagram shows as 148.6º. To simplify things, imagine extending a straight 180º baseline under the edge of the frame. The angle between that line and each leg of the frame at point D is:

(180 - 148.6) / 2 = 15.7º

This is the angle that each side of the knee makes with respect to the baseline (see the dashed line ML on the following diagram). It’s easier to draw the knee starting from the opposite side, which is parallel to that 180º baseline (AC), as we can use the plywood edge for this.

Frame B - Point D - Knee diagram

According to the plans (especially the diagram for Frame C), each knee has a width of 18 cm. So, I began by marking two vertical lines spaced 9 cm from a central line. These represent the outer edges of the knee, as well as its central axis. In my own diagram, I’ve labeled these as segments AD, BE, and CF to make it easier to follow.

Vertical lines 18cm - easy with the carpenter square

Next, I needed to mark the angled edges of the knee—segments like IJ and GH. These correspond to the edges of the frame, and their length matches the width of the pine strips used for the frame, which is 5.5 cm.

Now here’s the trick: these lines are perpendicular to the frame edges, so they are angled 15.7º away from the central line. That’s where trigonometry comes in.

We know:

• The hypotenuse (IJ or GH) is 5.5 cm

• The angle from the central line is 15.7º

Using basic trigonometry:

• The length along the axis (IA or GC) = cos(15.7º) × 5.5 cm

• The perpendicular offset (AJ or HC) = sin(15.7º) × 5.5 cm

Plug those into your calculator (make sure it’s set to degrees!):

• IA = cos(15.7) × 5.5 ≈ 5.29 cm

• AJ = sin(15.7) × 5.5 ≈ 1.49 cm

With those values, I measured and marked points I and G, then drew the two outer edges IJ and GH.

Segment GH

The final step is drawing the inner edges IK and GK—these are lines at a 90º angle from the outer edges, meeting at the midpoint between I and G. They complete the rectangular triangle shape of the knee joint.

Frame B - Point D - knee results

This method might sound a bit technical, but it’s quick once you get the hang of it—and it saves a lot of guesswork. Plus, it’s easy to replicate for the other frame joints using just a strip of plywood and your reference angles.

Points I and G are very easy to mark with the combination square

This kind of hands-on geometry feels very satisfying—it's not just about cutting wood, it’s about understanding the shape of the boat as it comes to life.