Question

I asked this kind of question last week and didn't receive the answer I was hoping for.

Answer 1

The question I have right now is
"State whether the given measurements determine zero, one, or two triangles.

B = 84°, b = 28, c = 25 "

Answer 2

How do I know when The 3 measurements can give 1, 2 or no triangles?

Answer 3

I know a triangle cannot be made when something like a + c < b

Answer 4

have a look at this article

http://www.regentsprep.org/regents/math/algtrig/att12/lawofsinesAmbiguous.htm

Answer 5

In this article they say:
Angles could be 30, 53, and 97 : sum 180
The angle from Quadrant II could create angles 30, 127, and 23 : sum 180

because 180 - 53 = 27?

Answer 6

I know sin( x - 180) = sin x

Answer 7

Or is it sin( 180 - x ) ?

Answer 8

it's sin(180 - x) = sin(x)

Answer 9

Ok. So for my problem I got
A = 84 B = 62.6 C = 33.4

Answer 10

I dont know where to go from here

Answer 11

you should have something like

sin(C)/c = sin(B)/b

sin(C)/25 = sin(84)/28

as part of your steps

Answer 12

yes

Answer 13

I'm getting this

sin(C)/c = sin(B)/b
sin(C)/25 = sin(84)/28
C = arcsin(25*sin(84)/28)
C = 62.618755

so I'm not sure how you got C = 33.4

Answer 14

Drawing

Answer 15

I got that too but 84 + 62.6 + x = 180

Answer 16

I mean A is 33.4

Answer 17

oh ok, so that's the angle for A (not C)

which means

A = 33.4 (approximate)
B = 84
C = 62.6 (approximate)

Answer 18

yeah you beat me to it

Answer 19

How do I know how many triangles can be formed though?

Answer 20

there's another possible angle for B, but the question is: does it make a triangle?

you'll have to consider angle A and C

Answer 21

Why B?

Answer 22

oh my bad, I meant C

Answer 23

there's another possible angle for C, but the question is: does it make a triangle?

you'll have to consider angle A

Answer 24

Why are you picking A?

Answer 25

ok ignore A for a second

Answer 26

we found that C = 62.6 (roughly)

what is another possible value of C?

Answer 27

117.4

Answer 28

so if C = 117.4 (roughly), then what is angle A?

Answer 29

Im not sure

Answer 30

we know B = 84

Answer 31

B = 84 doesn't change

Answer 32

only A and C are allowed to change

Answer 33

62.6 - 54.8 = 7.8

Answer 34

A+B+C = 180

A = unknown
B = 84
C = 117.4

Answer 35

A + B + C doesn't equal 180 then

Answer 36

if B = 84 and C = 117.4, then what is A?

use A+B+C = 180

Answer 37

117.4 + 84 > 180

Answer 38

A must be -21.4

Answer 39

since you can't have a negative angle, that means the other triangle is not possible

Answer 40

Oh ok

Answer 41

so only one triangle is possible and that's with

A = 33.4
B = 84
C = 62.6

Answer 42

Thanks

Answer 43

np