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#### RayZorback

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Hey woodworking gurus. I am a n00b to wood working but I am trying to learn to do a lot more things myself. I didn't grow up working with my hands much.

1st on the docket is a 2 dog, doghouse. As I am drawing up the plans and creating a cut list I have run into a snag and I can't figure out how to calculate a specific angel.

1st, let me say I'm a little perturbed that a 2x4 is actually a 1.5 x 3.5 and a 4x4 is 3.5 x 3.5. HOWEVER, my 4x8 sheet of plywood is 4x8! What is up with that?

And now for the math problem:
The front of the doghouse is 36" tall.
The back is 30" tall.
The width of the floor is 40" x 72".
The width of the roof is 43 x 75.
My goal is to "frame" the roof with a 2 x 4 (1.5 x 3.5) that sits with the 3.5" flush against the dog house - like a "lid".

The math problem: What angle is created when you have a 6" difference in height over 40"? I believe that I will need to make 1 angled cut on the 2x4 in the front of the dog house (on the 1.5" side). What is that angle? and how did you calculate that??

If you see any errors, please feel free to point them out. I am just trying to learn how to do a little more for myself! Thanks!!

#### minuteman62-64

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OK, see if I understand your question. You have a horizontal distance of 40" and a 6" rise at one end. You want to know the angle between the horizontal and sloped side? IOW, a right triangle with a base of 40" and a height of 6"?

Only way I know to do that is using trig. The tangent of the angle you want to determine is given by the opposite side (6") divided by the adjacent side (40"), or 0.15. The angle with a tangent of 0.15 is 8.53 degrees. All easily determined using a calculator with scientific functions - such as the one included with MS Windows.

I'm guessing some of the guys on this site have some neat ways of doing this calculation without doing the trigonometry - or can explain it better than I can. Hopefully we'll all get the same answer

#### johnep

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##### johnep
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If you design on sketchup. Will get a cutting list.
johnep

#### Manuka Jock

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1st, let me say I'm a little perturbed that a 2x4 is actually a 1.5 x 3.5 and a 4x4 is 3.5 x 3.5. HOWEVER, my 4x8 sheet of plywood is 4x8! What is up with that?
:icon_smile: Welcome to the world of wood.

The 2x4s are actually Ex 2 x 4 .
They were rough sawn at the mill 2"x4" and then , timber being what it is , it immediately starts to lose moisture and shrinks , with or without human assistance, unevenly .
In time they are machined to the reduced measurement .

As for the sheets , you have yet to come across 'joiners sheets' . The metric 'joiners sheets' "8' x 4's" are 2440mm x 1220mm , and the 'standard ones' are 2400mm x 1200mm

#### jschaben

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Not to add to your frustration but while your 4x8 sheet of 3/4" plywood may be 4' by 8' it is likely only 23/32" thick..... Welcome to the forum.:blink:

RayZorback

#### Manuka Jock

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Not to add to your frustration but while your 4x8 sheet of 3/4" plywood may be 4' by 8' it is likely only 23/32" thick..... Welcome to the forum.:blink:
:laughing:

#### cabinetman

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I don't like doing all the math...it makes my head hurt. I draw the project out full size on wrapping paper. If it's too large, I'll scale it down by half, or quarters to make it fit smaller paper. You'll get the same image but smaller, and it's easier to measure the angles with a protractor.

.

#### woodnthings

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##### where's my table saw?
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simple math .....sorta

You can use trigonometric functions to determine the length of the legs in a triangle that has a 90 degree angle. In your example the short vertical leg is 6". the longer adjacent side is 40" ..you want to know the angle in degrees... If you divide the side opposite the angle by the side adjacent to it you get a decimal result. This ratio is called the TANGENT of the angle.
6 divided by 40 = .1500 In a book of trig functions or online you can plug in that .15 and ask for the angle.. Look at this chart at between 8 and 9 degrees ...
http://www.math.com/tables/trig/tables.htm

Here's a link to help make it easy to understand.
http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent.php

EDIT!
TANGENT replaced sine...
Sorry for the mistake, cable is OUT:furious:
I'm on Dial Up for now...suks...:thumbdown:

RayZorback

#### minuteman62-64

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You can use trigonometric functions to determine the length of the legs in a triangle that has a 90 degree angle. In your example the short vertical leg is 6". the longer adjacent side is 40" ..you want to know the angle in degrees... If you divide the side opposite the angle by the side adjacent to it you get a decimal result. This ratio is called the sin of the angle.
6 divided by 40 = .1500 In a book of trig functions or online you can plug in that .15 and ask for the angle.. Look at this chart at between 8 and 9 degrees ...
http://www.math.com/tables/trig/tables.htm

Here's a link to help make it easy to understand.
http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent.php
It may be a matter of assumed orientation. Assuming a right triangle where the 40" dimension is horizontal, and the 6" dimension is vertical, 6 divided by 40 represents the tangent. The sine would be the 6" dimension divided by the hypotenuse - the sloping line, slightly longer than 40", between the start of the horizontal line and the end of the vertical line.

Also, it occurred to me that there may be a clever way of solving his problem using a framing square - way beyond my skill set.

#### Dave Paine

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As stated, simple trigonometry.

Rise (opposite angle) = 6

Then look up the number in the chart linked by WoodnThings.

If you have a spreadsheet try
=DEGREES((ATAN(6/40)))

Spreadsheet trig functions return a value in RADIANS, so you need another function DEGREES to convert RADIANS to DEGREES.

8.5 deg.

#### DonG1947

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Forget all the math!!! I'm with Cabinetman.

On your garage floor, basement floor, driveway, neighbors driveway, where ever, draw two parallel lines 40" apart. use a straight edge to connect to tops of the 2 lines.. Extend one line up 6". Now connect the taller line with the shorter line. That line represents the roof angle. Now do a direct measurement of the angle with a sliding bevel guage (Cheap and available at the big box stores). Use the guage to mark the angle on the 2x4 and cut, or use the guage to transfer the angle to your saw's miter guage.

Picture did not come through. Look up "sliding bevel guage" in Google images if you are unfamiliar with that tool.

Or you can get smaller, less demanding dogs and use a nice milk crate:laughing:

Don

#### jbsjbs

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I concur with the real-world mockup, but where math is needed Google's also got a great built-in calculator.

tangent of (6 over 40)

8.66 degrees

The built-in google conversions are pretty amazing. Where else could you so quickly learn that:

123 furlongs in nanometers

equals 2.4743664 × 10^13 nanometers

It used to take me hours to convert furlongs to nanometers, but not any more! ;-)

EDIT: In case the head scratch below was for me, let it be noted that the furlong to nanometer part was a joke. Accurate, but a joke. Just meant to illustrate the exhaustive nature of Google's built-in conversions and calculator.

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#### BassBlaster

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Unless somethng has changed over the years a 2 X 4 is 1 3/4" X 3 1/2"

#### Manuka Jock

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Unless somethng has changed over the years a 2 X 4 is 1 3/4" X 3 1/2"
Our 4x2 was 3.7/8" x 1.7/8" if I recall correctly.
Now a 4x2 is a 100 x 50 and is 97m x 47m .... approximately

:laughing:

#### woodnthings

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##### where's my table saw?
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There are situations where only math will work

Let's say you're on an airplane and need an answer before you land for the client. There is no room in the plane/car/train/truck to lay it out...

Let's say you're on the rifle range, you know the range is 500 yards. Your rifle is zeroed at 100 yards. How much do you hold over to hit the target at 500 yards? You need to know the bullet drop at 500 yards from a table or chart like this:
http://gundata.org/blog/post/308-ballistics-chart/

Let's say you are building an arch bridge across a pond and you need to have 6 ft of clearance above the water which is 2 ft below the grade. The bridge will span 40 ft from shore to shore. What's the radius of the arch..... Yeah, you could lay it out in a parking lot, but you'd need some tape measures, strings, calculator and other stuff.

Trigonometery is relatively simple when used with right angle triangles. You still need a function chart or scientific calculator or an online calculator. I like this site for it's simplicity: http://gundata.org/blog/post/308-ballistics-chart/

tc65
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