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Episode 17 – Triangle & Complementary Angles

A right triangle (90 degree corner) and the two complementary angles

In this post I talk about a right triangle and complementary angles.  I also show how this knowledge can be used to make a fixture to solve a real life problem.  No measurements are used, just angles are copied.

The first picture shows a right triangle and the two complementary angles.  Angle A and angle B have to add up to 90 degrees and so it is said A is complementary to B.

In the next  picture I show the actual problem I needed to solve.  The  base of my seed starter was flexing too much in the lengthwise direction, so I needed to add a brace.  Notice the wood is splitting on the one board and would have eventually failed completely if I had not solved the problem.

If you notice the faces of the two boards I am running the brace between; one board is facing upwards and the other is facing to the right of the picture.  If you use your imagination and extend lines of the two faces until they intersect this will form a right (90 deg or square) angle.  The line at the top of the brace forms the 3rd side of the right triangle.  This means the two angles I have to cut are complementary angles.



The brace I needed to install.

Fixture used to mark the complementary angle. The framing square forms the right angle of the right triangle.

Copying the existing cut angle of one end of the board.

Marking the complementary angle on the other end of the board.

Marking the mouth cut.








The picture to the right of this shows the fixture I used to mark the complementary angle.   This consists of 2 small C-clamps, a framing square and a nice straight piece of small lumber.  Notice how the C-clamps are positioned to stay out of the way of taking the measurements.



The scrap board I was using for the brace already had one angle cut, so I used the fixture to match that angle and then tightened the C-clamps so the straight-edge board would not slip on the framing square.  Notice I am matching the angle on the narrow ruler side of the framing square.



I then use the wide ruler of side of the framing square to mark the complementary angle on my scrap board.






The final step was to mark the  “mouth” part of the cut using a scrap piece of 2X4 as a guide.  I then cut the mouth out by using a saber-saw and cutting along the lines to produce the brace shown in the 2nd picture.   There is more detail on how this was done in the audo file.




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