Hello all,
I have the following problem:
The values in blue are known. So C is known, F is known, and the relation between angles S and T is sin(T)=1.3·sin(S).
I've drawn in the dotted lines, as I think I need angle R to solve this.
I know it's solvable, if I draw this in AutoCAD and put in values with the equation of S and T, angles immediately gets calculated. However, I need to do this for arbitrary values of C and F, so I really need the equation. Not the answer.
But I'm stuck. I tried to find the relation between trian- gle V and W, but to no avail.
I did find out that:
- B/A · 1.3 = E/D
- the area described by the dashed lines is the sum of area V and W. So:
- B2+C2=A2 and E2+C2=D2
- tan(R) = tan(S) + tan(T)
I can rewrite that to:
tan(R) = sin(S)/(1-2·sin(S/2)2) + (1.3·sin(S))/sqrt(-1.69·sin(S)2+1)
But I don't know how I can rewrite that equation to solve for S, if possible at all. But maybe I'm in the wrong path here.
If I can solve for one of the unknowns, I can solve for every other unknown.
Could anybody help me out?
Thanks in advance,
Erik
I have the following problem:
The values in blue are known. So C is known, F is known, and the relation between angles S and T is sin(T)=1.3·sin(S).
I've drawn in the dotted lines, as I think I need angle R to solve this.
I know it's solvable, if I draw this in AutoCAD and put in values with the equation of S and T, angles immediately gets calculated. However, I need to do this for arbitrary values of C and F, so I really need the equation. Not the answer.
But I'm stuck. I tried to find the relation between trian- gle V and W, but to no avail.
I did find out that:
- B/A · 1.3 = E/D
- the area described by the dashed lines is the sum of area V and W. So:
- B2+C2=A2 and E2+C2=D2
- tan(R) = tan(S) + tan(T)
I can rewrite that to:
tan(R) = sin(S)/(1-2·sin(S/2)2) + (1.3·sin(S))/sqrt(-1.69·sin(S)2+1)
But I don't know how I can rewrite that equation to solve for S, if possible at all. But maybe I'm in the wrong path here.
If I can solve for one of the unknowns, I can solve for every other unknown.
Could anybody help me out?
Thanks in advance,
Erik