Question

Please please please help

State whether the given measurements determine zero, one, or two triangles.

A = 58°, a = 25, b = 28

Answer 1

You need to find at least another angle.

Answer 2

You could use law of sines.

Answer 3

B=71.77100453...?

Answer 4

@Brittni0605 is that right? Thanks for your help so far

Answer 5

I'd like to see your work.

Answer 6

25/sin58=28/sinb

25/sin58

28/ANS

sin-1(ANS)

= 71.78

Answer 7

Ok, yes.

Answer 8

Thanks. So how do I use that to determine whether the given measurements determine zero, one, or two triangles

Answer 9

What is the supplement angle to 71.78 degrees?

Answer 10

I have no idea how to find that

Answer 11

180-71.78 = ?

Answer 12

oh. 108.22

Answer 13

Good, so:

Answer 14

ok so its like the ambiguous case?

Answer 15

Yes.

Answer 16

Since you know, one angle is 58. You have to check if the two possibilities for angle B are reasonable.

Answer 17

so i do 25/sin58=28/sin71.78 and again with 25/sin58=28/sin108.22?

Answer 18

No, you know all the angles in a triangle add up to 180, right?

Answer 19

yeah

Answer 20

So that means angle a, b, and c should sum to 180. you know angle a is 58. you have two possibilities for angle b, and well you dont know angle c.

Answer 21

but since you know two angles, they cannot add to 180 bc you have another angle in the triangle. So to check if the two numbers for angle b are possible, you must..?

Answer 22

add them?

Answer 23

so only one is possible?

Answer 24

because they equal 180?

Answer 25

180 - (71.78+58) = ..
180 - (108.22 +58) = ..

Answer 26

50.22 and 13.78

Answer 27

Ok, so both are possible. Angle c could be 50.22 and 13.78..

Answer 28

oh. so two are possible?

Answer 29

Yes.

Answer 30

Thanks. I think I actually get this a little better now. Thanks a ton.

Answer 31

No prob.