goal of law of sines
find misssing measures in an oblique triangle
oblique
not right
law of sines works when
ASA AAS SSA BUT NOT SAS OR ASS
law of sines
sinA/a=sinB/b=sinC/c or inverse
law of sines trick
look for pairs across
why is using law of sines when given two sides and an angle not straight forward
inverse sine only givesa acute angle, need to check for obtuse
ambiguos case
given A,, a, b or equivalent of SS
ambiguos A is acute
solve for B
possibilties
ambiguos A is obtuse
a>b 1 triangle
a<b 0 triangles
ambiguos A is acute possibilites
B i undefined because b is shorted than height (0 triangles)
Bi smallerthan A (1 triangle)
B is larger than A (2 trianges) so use B and 180-B
ambiogus check that
twi angles dont equal 180
what measures would casue two triagnles
solve all and check
even if sketches have same values
use 180-
law of cosines
a^2=b^2+c^2-2bcosA
switch around
law of cosines can be used to solve a triangle when
SSS or SAS
law of cosines when SSS
find largest angle first
use law of sines to continue solving
do smaller angle first
make sure
longest side is opposite biggest angle etc
why in an acute triangle c^2<a^2+b^2 and obtuse is opposite
when they are equal, its a right triangle
-cos really means positive
trangle angle formulas
given SAS or SSS
trangle angle formulas SAS
A=1/2absinC
A=1/2bcsinA
A=1/2acsinB
trangle angle formulas SSS
heron’s formula
s=semiperimeter
s= (a+b+c)/2
A= √(s(s-a)(s-b)(s-c))
bearing
an acute angle formed by the north/south line
each bearing has three parts
letter (N or S)
acute angle measure
letter (E or W)
