Question

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

C = 38°, a = 19, c = 10

Answer 1

@mathmale Can you help me? :D

Answer 2

Hello!

I got two help requests at the same moment, yours and someone else's, so feel obliged to divide my time between the 2 of you.

Have you tried sketching this triangle? Note that we don't know yet whether its an "acute triangle" or an "obtuse triangle."

Answer 3

Try to draw it "to scale."

Answer 4

Okay, like this?

Answer 5

Wow, oh wow! One of the nicest diagrams I've yet seen here!

Answer 6

b would be like 16.16. Right?

Answer 7

Thanks! I am a little confused, and I think this one might not be able to be done, because when I tried to do the SSA thing in my calculator, it said Error...

Answer 8

We need to work with the data given; neither b nor B is known.

Answer 9

We shouldn't try to figure those out?

Answer 10

C=38 deg, c=10, a=19, A=?? Ignore B and b for now. If the triangle can be solved, then we could find B and b later.

Write the Law of Sines, addressing only A, C, a and c

Answer 11

When I try to do A, my calculator says error. :(

Answer 12

\[\frac{ a }{ \sin A }=\frac{ c }{\sin C }\]

Answer 13

Which of these variables do we know? a? c? A? C?

Substitute what we know into the formula, above, which represents the "Law of Sines."

Answer 14

Yup, and you get sinA=(19sin38)/10, or A=arcsin(19sin(38))/10. RIght?

Answer 15

Try it. We need to know whether or not the result makes sense.

Answer 16

That's what I have been trying.. I get an error thingy.

Answer 17

You got an error thingy? :) ;) :)

Answer 18

Oh, hush. ;p So does that mean it cannot be solved using the Law of Sines? Because that's one of my choices.. :P

Answer 19

I didn't get an error thingy right off, but I did learn that sin A is supposedly 1.170.

Remember, the value of the sine function MUST be between -1 and 1. So, what can you conclude?

Answer 20

Please buy an error thingy and send it to me via Priority Mail.

Answer 21

So it's not a sine function?

Answer 22

I'll be sure to do that! :P

Answer 23

A) No triangle is formed.

B) A = 58.6°, B = 83.4°, b ≈ 15.6

C) A = 83.4°, B = 58.6°, b ≈ 15.6

D) The triangle cannot be solved with the Law of Sines.

Answer 24

Oh, thanks!!!

I wouldn't conclude that "it's not a sine function." It's just that the result you and I both got (an error thingy) is not permitted, because the value of the sine MUST be between -1 and 1. So your choice D is absolutely correct.

Answer 25

Yay! Thanks! I have a few more. :(

Answer 26

Go ahead and post them, one at a time. But remember, another student wanted my help at exactly the same time as u, so I have to go see whether he/she still needs it.

Answer 27

Haha. You're fine! Oh, and *you. ;P