Thread: maths help

If I remember correctly then
Tan of the angle is opposite over adjacent for 80 deg = 9.00365495
Sine is opposite over hypotumuse for 80 deg = -0.993888654
Cos is adjacent over Hypotumuse for 80 deg = -0.110387244

Then if the long side the hypotumuse =10 units the opposite side would 10 x -0993888 or 9.9388 units and the base would be 10 x .11038 or 1.1038 units long
or to simplify use a protractor and make a jig

Originally Posted by Gaza

what lengths work so that my angles are 90deg 90deg 10deg

I assume you mean 80 - 90 - 10, as per your diagram.

I don't think there is any 'nice' numbers that work for those angles. 3-4-5 is a special case that has more to do with Pythagoras than woodworking. If your two sides are a and b, with a the shorter side and h the hypotenuse, then some basic trig gives you...

Sin(10°) = a / h = 0.173648178
Sin(80°) = b / h = 0.984807753

Therefore
a = 0.173648178 * h
b = 0.984807753 * h

Got a good lowest common denominator algorithm?

thanks guys,

it is to set out a wall so a protractor might be a bit small,

any other ideas

afaik, you only get a pyhtagorean triad when you have a traingle with sides of 3,4,5 equal units, and one other combination.

So, if you have a right angle tri with 2 sides, 1 is 3u and the other is 5u, then the other side is going to be 4u, but 5u will be the hypotenues.

To get a triangle with an angle of 10deg, the hyp. would have to be very long. I cant remember the calc, but you might be able to find a web based calc you can put a series of figures into, ie, your angles and away you go.

Chris

90, 80, 10 is still a right angle triangle so Pythagoras still works but not 3,4,5

Pythagoras states that the square of the length of the two adjacent sides will add together to equal the square of the hypotenuse. In the case of 3,4,5

3 squared + 4 squared = 5 squared
9+16=25

So just do the calculation by squaring two of the lengths you have to find out what the other is and then hey presto you have a 90, 80, 10 triangle.

If the shortest side (opposite the 10 degree angle is exactly one metre then the longest side (opposite the 90 degrees is 5.7588 metres and the side opposite the 80 degrees is 5.6713 metres

See the attached diagram.

The ratio of numbers is 1 : 5.6713 : 5.7588 or 1 : (1/tan10) : (1/sin10)



Cheers,

Chipman

You can also double the 3, 4, 5 known as the golden ratio to 6, 8, 10 or tripple to 9, 12, 15 etc.
SB

Originally Posted by Superbunny

You can also double the 3, 4, 5 known as the golden ratio to 6, 8, 10 or tripple to 9, 12, 15 etc and still have 90, 80 and 10 degrees.
SB

Sorry, but none of the golden ratio options (double, tripled, quadrupled or whatever else) will ever give 90, 80 and 10 degrees. You need to use Pythagoras's' theorem I mentioned above by taking the measurements off the two walls that have a known angle you want (the 80 or 10 degrees) from construction plan. Look at the ratio Chipman gave you, it is correct and his ratio will never fit into the golden ratio.

The golden ratio comes from Pythagoras but is not transferable to all right angled triangles, it is just one option that is commonly used in construction because of the nice even numbers.

Chipman goes to the top of the class!!

Originally Posted by gracoope

Chipman goes to the top of the class!!

Yes, he does. Another reminder: The interior angles of any triangle of any form must sum to 180 degrees; otherwise it doesn't close.

Joe

Actually, I would be really embarrassed if I got it wrong.....

after all, I am a science & maths teacher


Regards,

Chipman