Question

A=40 degrees, C=75 degrees, c=20 does it make one triangle, two triangles, or no triangle?

Answer 1

Do you know total degree in a triangle?

Answer 2

yes its 180 which mekes angle B=65 degrees

Answer 3

then I use law of Sines to get b/Sin65=20/sin75

Answer 4

please give me a sec to put this in my calc

Answer 5

alright So I got b=18.55

Answer 6

So do i just do like the same thing to get A?

Answer 7

yes and from there you could solve for a ....but this only gives you 1 triangle with 3 distinct angles/sides

Answer 8

So how exactly do you know if it equals one triangle or two?

Answer 9

WaIT! so do I do C/sin c= A/sin a or B/sin b= A/ sin a?

Answer 10

i believe its from solving for the angles...sometimes you may get a situation where when solving for an angle using Law of sines, there will be 2 possible answers

example
\[\frac{\sin A}{3} = \frac{\sin 30}{4}\]
\[A = \sin^{-1} (\frac{3\sin 30}{4}) = \sin^{-1} (\frac{3}{8})\]

Answer 11

also, by AAS congruence theorem, only one triangle is possible given a set of fixed Angle Angle and Side (40, 75, 20)

Answer 12

yes to find any side or angle, you can use Law of Sines
\[\frac{a}{\sin A} = \frac{b}{\sin B}= \frac{c}{\sin C}\]
or
\[\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}\]
doesn't matter

Answer 13

okay so now I just want to know how you know for sure if its one triangle or two or none

Answer 14

look at example i did in earlier post...notice there will be 2 solutions for angle A
this means there are two possible triangles

Answer 15

alternative of law of sines you can use,

congruency theorems + triangle inequality theorem :


congruency theorems :
AAS : exactly one triangle
ASA : exactly one triangle
SAS : exactly one triangle
SSS : exactly one triangle

apply triangle inequality theorem for below :
SSA : exactly two triangles
rest : infinity/none

Answer 16

Alright so I have one saying it's one triangle and another saying it's two, so Who's right?

Answer 17

dumbcow is referring to previous post.... not this one

Answer 18

angle A is given here,

Answer 19

oh okay so how did he get two answers? Cuz I don't get how he got sin^-1(3/8)

Answer 20

hmm im not following law of sines....
im for congruency theorems, they are more intuitive and look simple to me

Answer 21

okay yeah that looks simpler to me too except for how SAS is one triangle while SSA is two

Answer 22

if SIDE, ANGLE and SIDE are fixed in that order,

its obvious that only one triangle cuz, you cant do anything here, except connecting the two segment ends, right ?

Answer 23

yeah So if I has SSA how do you get two?