Expert: Sherry Wallin - 4/27/2011

Question
QUESTION: Hi there

When working out rafter lengths in the building trade we are taught half span divided by cos degrees equals rafter length, Thats fine if you have a calculator with cos, so how do you do it with out the little cos button on your calculator?

6m wide house would calculate  1/2 span= 3m  so 3m divided by cos degrees equals rafter length
example 3m divided cos 30 equals 3.464

SOH CAH TOA, cos is adjacent over hypotenuse,
How can you work out the length of hypotenuse using the length of hypotenuse?

ANSWER: Hi Joss~

I didn't answer your question because what you say does not make mathematical sense to me. Did you really mean "How can you work out the length of hypotenuse using the length of hypotenuse?" If so, then I think you mean is there an equation with the length of the hypotenuse in it that will help you find the length of the hypotenuse. You already mention SOHCAHTOA so I presume you know what each of those letters mean. If you know the measure of the angle that is made with the rafter and the span and you know the measure of the half span and you want to know the height (the height from the center of the span making a right angle with the peak of the roof) then you would have to have the length of the hypotenuse to say that the length of the hypotenuse times the sin of the angle is the height. If you know the height and you know the half span length you can use pythagorus theorem a^2 + b^2 = c^2 where c is the length of the hypotenuse and a is the height and b is the length of the half span. If you know the length of the hypotenuse c, and you know the angle the rafter makes with the half span, call x, then you can get either the height b, or the length of the half span a, in following way respectively: b = c*sin x or a = c*cos x

Math Prof

If this still isn't clear, draw a picture, label it, and tell me what it is you are trying to find out. If you need to find out how to get the angle please specify that too.

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QUESTION: Ok sorry,( and you'll have to excuse me as i don't know the proper terminology)
If i was to work out the length of hypotenuse with only    - Length of adjacent ('A') and degrees (no length of opposite ("B")
Say length of adjacent ("A") was 1.732       1.732 divided by cos30 would equal 1.9999 which is length of hypotenuse ("C")  so to work out cosine you would divide adjacent by hypotenuse,("A" divided by "C") which is 1.732 divided by 1.9999 equals 0.866.
So if 0.866 is cos, how do i use 0.866 to get length of hypotenuse ("C")  1.9999?  
Trying to understand how to work it out with a calculator or a cosine table.

Answer
Joss~

Aha!

Now I know what you want. There is a key on your calculator that either says cos^(-1) (cosine inverse) or arccos (arccosine). It will be above your cosine key, usually you need to use the '2nd' key and then push cos when you have the degree of an angle from the cosine function. When you get the cos x or sin x or tan x, x is the angle measured in degrees. In order to get a number that is a length you will always need to use the inverse key regardless if it is sine or tangent, just match it with the 'type' of trig function you used, i.e., cos^-1 if you used cos x, sin^-1 if you used sin x, or tan^-1 if you used tan x.

Math Prof