I'd like to build a porch bench. it's to have legs that angle outwards. But everywhere I've looked gives me the height. And I need the length of the legs.
Can someone show me the calculation for calculating the length of the legs to arrive at an 18" height on an 11-degree angle.
Seeing heavy-duty arithmetic is not my strong suit, if you were to show me template for the calculations, I'd sure appreciate your help for future self-induced brain problems.
a2 + b2 = c2, where the latter is the hypotenuse or longest leg and a and b form a right angle. So you want the square root of the width of the leg space squared plus the height squared.
Usually in a situation like this I'll just make a full sized drawing on my tablesaw outfeed table that has a white formica skin. My 2nd choice would be to make the table with the legs 21 or 22" long, dry assemble, then mark the legs and cut to length. Having re-read this, after making my full sized drawing I'd cut the legs a couple inches too long just because, then dry assemble and mark and cut to final length. Sometimes my drawings just don't quite turn out as accurate as they should.
It's a simple trig calculation using sin or cos of the angle, depending on how you think of it. Well, it's simple if you know how. I have to get up at 2am so I can't calculate it now but there are easy right angle triangle calculators on the web like this one: https://keisan.casio.com/exec/system/1273849674
Sketch the floor, leg, and height and angled leg and select the option that corresponds to your diagram and enter the values.
Your question could get quite involved if there are 4 legs at compound angles, versus 2 slab-type legs. Or if the legs are tapered and you want a template for cutting.
But basic trig gives you a clue at least on how to approach....you have an 11 degree angle, with adjacent side= 18”, and you want to know the leg length or hypotenuse, all measured in a plane parallel to the bench length.
So, the clue is,
Cos(11) = 18/leg length
Leg length = 18/cos(11) = 18/0.95 = 18.95”.
But. If you have 4 legs splayed, need more info as to angles. And if you want a dimensioned drawing of the leg, need more info.
Draw a right triangle. Label the height H and label the hypotenuse L, where L is what you want to determine and H is 18". The angle at the top of this triangle is 11 degrees.
Since this is a right triangle, cosine (11 degrees) = H/L.
If you have a pocket calculator, enter 11, then tap cos and you will see that the answer is .98.
So .98 = H/L, or rewriting this you have L=H/.98.
Substituting for H, L=18/.98 = 18.33.
I see you have a bunch of answers already, but I agree with Mark.
Just a note on the assembly of the legs into the seat. It is not a good idea to cut the legs to the computed final length because the leg bottom will not be flat to the floor.
I suggest that you cut the legs 3/4” long and dry fit them into the seat. Prepare a scrap piece of 3/4” plywood about 6” square by drilling a hole in the center just large enough for the bottom of a leg to go through. Then with the seat and legs standing in an upright position on a flat surface place each leg, one at a time through the hole in the ply wood and using a Japanese style dozuki saw cut the leg length using the flat surface of the plywood as a guide. After each leg is shortened by 3/4” shim it with scrap 3/4” ply before moving to the next leg to cut it.
This will result in a good flat leg/floor interface all around with the seat at the desired height.
They tacitly assume an infinitely thin leg or one that doesn't set flat on the floor. A leg with thickness must have an angle cut on each end to sit flat on the floor and intersect the bottom of whatever. Hence, the cross section will be a parallelogram with a center line being the length others have calculated but the starting length that this leg is cut from must be longer. The correct blank length can be calculated by those familiar with geometrical calculations but in this case......draw it out.
