# Can some explain why?

• Jul 28th 2011, 06:12 AM
DamenFaltor
Can some explain why?
This might be fundamental, but I can't explain this...

Having a triangle with side a=4, b=8 and A=30 degrees.

Using the Law of Sines, you can determine that this is a 30,60, 90 triangle.

Why is it that there is only one triangle possible? I was explained that when you use the law of sines to solve for a missing angle, you need to then check to see if there are other triangles possible by doing the following. (using the above example)

B = 90 degrees. 180 - 90 = 90. 90 + 30 (the measurement of A) = 120. 120 < 180 and therefore, normally, there would be 2 triangles possible.

However, my textbook says that there is only one triangle possible. Our teacher told us "That's the way it is with 90's" - which tells me nothing. Either I've done something wrong, or there's a principle I don't understand. Can someone explain?

Thank you!!
• Jul 28th 2011, 06:52 AM
Siron
Re: Can some explain why?
Do you mean the angle A=120°?
• Jul 28th 2011, 07:43 AM
DamenFaltor
Re: Can some explain why?
yes 90 degrees + 30 degrees = 120 degrees. If this is less than 180 degrees, ( as was explained to me) this indicates that another triangle solution could be found.
• Jul 28th 2011, 07:52 AM
Siron
Re: Can some explain why?
But if A=120° then you don't have a right-angle triangle anymore and so the Law of the sines doesn't work. Wat would be the measure of the other angles in a triangle with A=120° along you?

EDIT: Forget this post, I'm from Belgium so I didn't realise what the 'Law of the Sines' is. Now I do, so this post doesn't make sense.
• Jul 28th 2011, 08:10 AM
DamenFaltor
Re: Can some explain why?
The original problem is this: a=4, b=8 and A=30 degrees.

which gives a 90 degree right triangle.

When you use the Law of Sines to get an Angle, there is a possibility that there are multiple triangles that the above measurements can be part of. Our professor told us that the way to determine if there are multiple triangles was to do this: Lets say you are solving for angle B.

$\frac {sinB}{8} = \frac {sin(30)}{4}$
with algebra:

${sinB} = \frac {8 * sin(30)}{4} = 1$

arcsin(1) = 90 degrees.

ok so now, we know that the angle of B is 90. But how to determine if there are any other triangles? The formula is:

y = (180-B) + A. If y is less than 180, there is another possible triangle.

So since we've determined that B is 90 degrees:

(180-90)+30 = 120. 120 < 180.

However, the book states that there is only 1 triangle possible for a 90 degree right triangle. What I want to know is why?
• Jul 28th 2011, 08:17 AM
Siron
Re: Can some explain why?
modified.
• Jul 28th 2011, 08:25 AM
DamenFaltor
Re: Can some explain why?
Yes I realized I typoed part of it. I'm really having a hard time getting latex right, and I tend to screw up the problem trying to get it to look right. It is correct now.
• Jul 28th 2011, 09:47 AM
Siron
Re: Can some explain why?
Indeed B=90° and with A given that implicates C=60°. If A is given then there's just one possibility for B and C.
In the formula you gave what is y?
• Jul 28th 2011, 09:54 AM
DamenFaltor
Re: Can some explain why?
y is just a variable that the professor made up to hold the result of the formula (180-B) + A