I need help with a pair of trigonometry problems.

October 11, 2018 2:09 PM

I'm making these workbench type sawhorses in two different different heights. I want one pair of sawhorses to be exactly 36 inches tall and the other pair of sawhorses to be exactly 30 inches tall (without the plywood tops). The problem is that the legs splay out at a 5 degree angle, so I don't know how long to make them.

Question A: Imagine a tall right triangle with a comparatively short base. The angles are 90 degrees, 85 degrees, and 5 degrees. The triangle is 30 inches tall. How long is the hypotenuse?

Question B: Imagine a slightly taller right triangle with a comparatively short base. The angles are again 90 degrees, 85 degrees, and 5 degrees. The triangle is 36 inches tall. How long is the hypotenuse?

I can find the formula, but I have no idea how to plug it and the info I know into the scientific calculator on my PC to get the correct answers.

Your help will be greatly appreciated!

posted by Daddy-O to Home & Garden (15 answers total)

Best answer: I like this triangle calculator. If I"m understanding you correctly, the hypotenuse for the 36" tall bench would be 36.138 inches tall when I put the angles and your one measurement (the desired height of the bench) into the calculator. It also shows that the base of the foot of the bench would end up 3.15" out from vertical, if that makes sense.
Try it out yourself and my apologies if I didn't understand correctly.
posted by purple_bird at 2:24 PM on October 11, 2018

For Question A: if you look at your triangle once you draw it you should see that the side opposite the 85 degree angle is 30 inches. Therefore since sine is opp side / hypotenuse, you get sin(85 degrees) = 30 inches / x inches (where x is the length of the hypotenuse). Solving for x you get x = 30 inches / sin (85 degrees) = 30.11 inches.
B is solved similarly: x = 36 inches / sin (85 degrees) = 36.14 inches.
posted by peacheater at 2:24 PM on October 11, 2018

Remember the thickness of the legs—depending on what you'll do with beveling the top and bottom ends, you may need to adjust for that. It sounds like you're attempting to be extremely precise with these sawhorses.
posted by lostburner at 2:33 PM on October 11, 2018

Response by poster: My goal is to use the horses as infeed and outfeed tables for my table saw, so I'm trying to make one pair the same height as the saw; and the other pair the same height as the saw, less the height of the torsion beams.

Thanks so much for the assistance. I'm bookmarking that triangle calculator!
posted by Daddy-O at 2:42 PM on October 11, 2018

Best answer: For all my Pythagorean needs, I go to the aptly-named triangle-calculator.com. It's the easiest-to-use of the online triangle calculators that I've found.
posted by Anticipation Of A New Lover's Arrival, The at 2:43 PM on October 11, 2018 [1 favorite]

Another way to get the same result:

Length (measured along one side) = height/cos(5).

So, cut a 5 degree angle on one end of the stock. Flip it over, end-for-end, and measure [height/cos(5)] inches from that freshly cut end, and make a mark. Cut the second end, making sure the angle you cut on the second end is parallel to the first end.
posted by jon1270 at 2:44 PM on October 11, 2018

But you know, what I would actually do in your case is build the sawhorses, then measure down to the height I wanted and cut the legs short to suit. I dunno about you, but personally I would probably not be able to build them precisely enough to get a perfectly flush surface height.
posted by Anticipation Of A New Lover's Arrival, The at 2:45 PM on October 11, 2018 [12 favorites]

2nd'ing Anticipation Of A New Lover's Arrival, The, if you watch a carpenter (like a house framer), that's exactly what they would do. Who has the time for math?

Build the sawhorses with intentionally too-long legs (go with 40"?), then flip them upside down, measure up from the floor to 36" high at the legs and mark a level line, then cut.

Do the same for the 30" sawhorse.

If you get it a little too short, then put an extra layer of 1/4" ply or whatever is needed on top to bring it back up to height.
posted by jpeacock at 3:13 PM on October 11, 2018

Also, check that your floor is actually level. I work in my garage, which has a decent slope to drain water from wet cars, etc, and I have some adjustable height infeed/outfeed tables that are set differently due to the floor slope.

You may not want exactly 30"/36".
posted by jpeacock at 3:16 PM on October 11, 2018 [3 favorites]

Nthing cut them after making them too long, like you would level up a chair.

Your floor will not be perfectly level, none are.
posted by deadwax at 9:29 PM on October 11, 2018 [1 favorite]

They look nice, but why angle the legs at all? On most sawhorses, you angle the legs so you can stack them, or want a narrow top. They don't look like you could stack them.

Maybe use these brackets? They're battleship strong. And you might want to think about locking casters, they make it a lot easier to move stuff.
posted by Marky at 10:46 PM on October 11, 2018

Speaking as a mathematician, I say eschew the trigonometry and lay them out flat on the floor. Also, check out brackets made for quick and easy sawhorse building at Home Depot, et al. Finally, a 5 degree spread seems very narrow and tippy.
posted by SemiSalt at 4:30 AM on October 12, 2018

Best answer: Given your desired use, I would cut the legs a little short, and throw some leveling feet on to allow you to dial these in super precisely.
posted by misterbrandt at 7:18 AM on October 12, 2018

Response by poster: Despite being super careful while cutting and assembling, the first sawhorse/workbench still wobbled a bit, as predicted by several people above. I'm glad I took misterbrandt's excellent suggestion to shorten the legs a bit and made provisions for adding leveling feet. The leveling feet make it a snap to level things up and bring it even with my table saw.
posted by Daddy-O at 9:20 AM on October 25, 2018 [1 favorite]

Response by poster: I finally finished the sawhorse workbenches and torsional beams.

The taller workbenches are the same height as my table saw so I can use them as infeed/outfeed tables. The shorter workbenches are the same height as my table saw when the torsional beams are on top of them so I can use them as infeed/outfeed tables too. One side of the torsional beams has a melamine surface for easy clean up after glue ups, and the other side has a non-marring Homasote surface to protect finishes and surfaces.

Big thanks again to Anticipation Of A New Lover's Arrival, The for the triangle finder link and misterbrandt's excellent suggestion to shorten the legs a bit and made provisions for adding leveling feet. Thanks again to everyone for your answers.
posted by Daddy-O at 11:10 AM on November 17, 2018