Laws/Relations

The laws are used for any triangle (doesn’t have to be a right triangle):

Formlerne 
Cosinusrelationer 
Til beregning af sider 
2 
c 
Sinusrelationer 
Til beregning af sider 
Til beregning af vinkler 
• b • c • cos (A) 
• c • cos (B) 
• b • cos (C) 
cos (A) = 
a2 + c2 — b2 
cos (B) = 
cos (C) = 
Til beregning af vinkler 
sin (A) sin (B) 
sin (C) 
sin (A) ¯ sin (B) ¯ sin (C) 
a 
b
l.aw οτ 
ΙΙΙ" — 
tan + )
s Formula 
o + b cos Ha —

Solving a triangle:
When you try to find a triangle using the laws, you might get two different triangles, because

You get two answers from a trig function, and they can be used to make two different triangles, but usually only the one that actually makes sense is the real one

Known variables:
sss, aaa, aas, ssa, sas
s = sides
a = angles
3 angles: no Solution, can’t be solved

Oblique triangles:
Just a triangle that isn’t a right triangle, and can be made into 2 right triangles

When to use the Law of Sines:
ASA and AAS can be used with the law of sines
And SSA can also be used but has either no solution, one solution of three solutions

When to use the Law of Cosine:
Can be used in SAS and SSS triangles

How the cosine laws are found: