Some help with trigo

[Anonymous]

I would apreciate some help for this trigonometrical problem.
I am searching for H or ang, function of X and ray. I don't find a solution.
Thanks to anyone for the highligth.

[James Murray]

Law of Sines. I think. Not that bad if I'm right.

a/SIN(A)=b/SIN(B)=c/SIN(C)

The angle we know, A=135. Opposite is the side we know, a=R.

The other side we know, c=ray.

You're looking for B.

R/SIN(135)=ray/SIN(C)

SIN(C)*R=ray*SIN(135)

SIN(C)=(ray*SIN(135))/R

C=ASN((ray*SIN(135))/R)

B=180-A-C.

Something like that.

[David Collins]

Unsolvable, I think.
X minus the endbit (and therefore H) could be be anything, depending on the value of ang.

[Frank Beister]

I think it's solveable, because the triangle over 'X' makes the figure stable.

SIN(ang)=H/R
SIN(ang/2)=s/R
X=d1+d2
d2=H*TAN(45)=H
TAN(ang/2)=d1/H or SIN(ang/2)=d1/(2*s) or COS(ang/2)=H/(2*s)

I have not the time to solve it, maybe later or someone else wants...

[Frank Beister]

Sorry, I haven't seen that James has the solution yet:

ang = 180 - 135 - ASN( ray*SIN(135) /R)

[Anonymous]

James wrote:
Law of Sines. I think. Not that bad if I'm right.

a/SIN(A)=b/SIN(B)=c/SIN(C)

The angle we know, A=135. Opposite is the side we know, a=R.

The other side we know, c=ray.

You're looking for B.

R/SIN(135)=ray/SIN(C)

SIN(C)*R=ray*SIN(135)

SIN(C)=(ray*SIN(135))/R

C=ASN((ray*SIN(135))/R)

B=180-A-C.

Something like that.

Thank you so much, James, you save me. It works perfectly.
The link posted by Bill is helpful, too. Thanks to all for your help.

[Vitruvius]

I think the formulae are:

H = X*SIN(45) --- X being the hypoteneuse of small triangle
Ang = ASN(H/R) --- and then plugged into the large triangle formula

Assuming from your diagram that X, RAY, and 45d are known values.

Cheers

[Anonymous]

Vitruvius wrote:
I think the formulae are:

H = X*SIN(45) --- X being the hypoteneuse of small triangle
Ang = ASN(H/R) --- and then plugged into the large triangle formula

Assuming from your diagram that X, RAY, and 45d are known values.

Cheers

Not exact, H = R*sin(ang)
For the rest, X, ray and 45 are known.

I did i first try with the sum of angles into a triangle, another one with pythagoras (Frank's example), without success.
I can assure you that James's solution works perfectly. The occasion for me to rediscover this "sine rule" (Bill's link).
Thanks anyway.