Expert: Jack Cheng - 12/10/2006

Question
Hi i can get an answer for this very simply with a calculator but need a way of getting it without one (including slide rules etc)
an engineer needs to run a taught cable from the top of a tall building to a small post 30m away from the base of the buliding the angle the rope makes to the ground is 75*, calculate the length of cable required.
The square root of 2 =1.4 and the square root of 3 = 1.7 can be substuted at the end of the equation. thanks for any help you can give

Answer
Hi Mark,

You basically need the cos 75*.

Unless I am mistaking it for something else, to use the slide rule, I think you need a special ruler-like device.

I don't know how to do this for any general trig. problem, but for this problem, it can be written as cos (45*+30*). You can then use the Addition Formula of cosine to solve it:

[FOR BETTER CLARITY, VIEW WITH A FIXED-SIZE FONT LIKE COURIER.]

cos (45+30) = cos 45 cos 30 - sin 45 sin 30
           = sqrt(2)/2 * sqrt(3)/2 - sqrt(2)/2 * 1/2
           = sqrt(2)/4 * [sqrt(3) - 1]
           = 1.4/4 * (1.7-1)
           = 0.35 * 0.7
           = 0.245

I hope this helps,
Jack