Building Confidence


Volume 22 Issue 1
ISSN 1923-7162


Welcome to Dave's Shop Talk's Home Improvement Newsletter of questions from our members on their construction projects, a Tip of the Month and a home remodeling article, both from our website at https://daveosborne.com. We are into our 21st year putting out this Newsletter. Dan and I would not be able to do this without your input every month. Thank you and keep the questions coming!

Tips of the Month

Be sure to check the required rough opening sizes of your windows with your salesperson to be sure they will fit your particular windows.

When laying out studs for a wall, be sure to layout both top and bottom plates at the same time.

Ask Dave!

The odd time I get requests from subscribers for, "How do you come to that conclusion". Sometimes my answer is based on Trigonometry, which is basically the ratios between the lengths of the sides of a right triangle (a triangle with one angle of 90 degrees).

Drawing of a right angle triangle showing the basic Trigonometry ratios of its sides.

In the diagram you can see that if the angle is small then the length of O divided by the length of H (ratio of O to H) is going to be small (because O gets smaller compared to H) and if the angle is bigger then O divided by H will also be larger.

There used to be books of Trig Tables which gave the ratios of the different sides for every size angle, but now we have $10 calculators that give this data (and with much greater precision).

We just need to know that a sine (generally abbreviated "sin" on a calculator and in formulas) is the ratio of the length of the side opposite the angle of the triangle you're working with divided by the hypotenuse (the side of the triangle opposite the right angle of the triangle).

In our case, we know that the angle is 25 degrees, so the calculator says the sine of 25 degrees is .4226, so we just plug that into the formula to calculate the length of the side opposite (which in this case is the total rise of the steps) and we have:

Length of side opposite = .4226 X 120' (the length of the slope our
    stairs are going to be on)
Total rise = 50.714 feet.

To calculate the total run of the stairs on the 120' slope we just use the formula to calculate the length of the side adjacent to the 25 degree angle. First we calculate the cosine (abbreviated "cos" on calculators) of 25 degrees, which comes to: .9063

Length of side adjacent = .9063 X 120'
Total run = 108.757 feet.

To check my figures I used good ole Pythagoras or what we call 3 - 4 - 5 method. Pythagoras discovered 2500 years ago that the longest side of a right triangle multiplied by itself equals the sum of the smaller sides each multiplied by themselves. From the diagram:

H x H = (O x O) + (A x A)

It's called the 3 - 4 - 5 method because a triangle with sides that have lengths in ratio of 3, 4 and 5 is always a right triangle.

5 x 5 = (3 x 3) + (4 x 4) or 25 = 9 + 16.

So, our long staircase down the 120' slope with a total rise of 50.714' and a total run of 108.757' should satisfy this formula:

120 x 120 = (50.714 x 50.714) + (108.757 x 108.757)
14400 = 2571.91 + 11828.085 which checks out.

Another useful thing to know about all triangles is that all three angles always add up to 180 degrees no matter what shape of triangle. Since one of the three angles of a right triangle is always 90 degrees then you know that the sum of the other two angles is always 90 (example, if one angle is 50 the other is 40).

Dave

Feature Article of the Month

(taken from our website: DaveOsborne.com)

Jigs 7: Woodworking Compass

In my woodworking career there have been numerous times I needed to scribe an arc or a complete circle, usually full size. For example, scribing the trim for a 6' wide circle head window with a 3' radius or making a template for rounding off the corners of a curved archway.

A handy idea to use for a large woodworking compass in the field, is to make a compass from a length of 1x2 or a similar size ripping. Yes, the yuppies use what they call trammel points, a point attached to a block and a pencil attached to a block with a specific sized stick of wood, or beam between them. The adjustment is made by sliding the ends along the beam to arrive at the correct radius. Well, although I have a pair of trammel points it's often faster to pick up one of the rugged and ever present sticks laying around a woodworking site. I measure the correct radius from the square end and drive a nail through it at this point. With my pencil always at the ready, I scribe the arc while the nail holds the center point fast into the piece of wood or plywood onto which I want the circle or arc drawn.

Here is a drawing of a simple woodworking compass:

Diagram showing how to use a compass to make a semi-circle top opening for a dog house with measurements.

Dave

Almost the End

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Dan and I wish all our readers and members of our website, all the best in 2023 and stay safe out there and thanks to our Front Line Workers.


Dave

(Ask Dave) (About Dave)



Your source for building tips, woodworking & furniture plans, house plans and building advice directly from Dave...

Hi, I'm Dave Osborne. With over 50 years experience as a journeyman carpenter, foreman and contractor in heavy construction I enjoyed working with apprentices and sharing the tricks of the trade that others shared with me. Now I get emails from Members all over the world and we include many of my answers in our Free Monthly Newsletters. Some of my answers include drawings and instructions specific to a project, but may also answer your questions. I use correct construction terminology, so you can confidently inform your building supply dealers or contractors exactly what you need.

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