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o-o some one would have to be a pro to figure that out...

It is trig Pre Cal

what grade you in?

College

Yes.
Are there choices? I can give you the answer.

oh wow

No choices. Let me see if I can make one up close to it.

h = 3.48

what is \(h\)

h is the height

This has to do with Sine Law

It has to do with Sine Law and figuring out if there is one or two triangles

height drawn from vertex A to its opposite base?

I am drawing a picture

|dw:1435185125370:dw|

|dw:1435185224437:dw|

|dw:1435185335223:dw|

But I am not sure what you want me to do. hehehe....

In my studies this is call the Ambiguous Case of (SSA) Side Side Angle

I think they are using the rule to differentiate between these two triangles:
|dw:1435187302571:dw|

With the triangle I have up there, these rules do not hold true.

Am I right? Those rules I have do not apply correct?

Now they apply to one of the examples they give with the rules, which is a=7, b=5 A=70

when they say "2 sides and an angle" do they mean the "included angle" ?

Yes, that is how I take it.

Looking at your rules (trying to make sense of them)
No Triangle = a

Correct

so the first two make sense. But note the angle is *not* the included angle between a and b

One Triangle a >=b and a> h=b sinA
I think your example that you entered up above fits this one.

and this one
Two Triangles = b>a>h=b sinA
means
|dw:1435189157259:dw|

A could = 159.6 because b=5 so 180-20.40 = 159.6+5 = 164.6 and C could = 180-164.6 = 15.4

But I have not drawn out the triangle to see what it looks like

I have to find A before the rules work.

Since they are using A but I have B the rule for me b>=a and b> h =sinB

Here is trying to make 2 triangles with a=40 and b=10

Here is the other way round, b=40, a=10
now we can make two triangles (see the red and blue lines)

Yes, we can create two triangles but I am wondering about the rules.

What is a problem you want to analyze using the rules?

|dw:1435191754375:dw|
To me it seems the rule is being applied like b >= a and b> h=a sinB

i.e A = 5, B is unknown , side a=10 , side b= 40

yes, you can relabel in the rules. But the idea is to be consistent.

Ty for you time!!!

yw

I sent you 20 owlbucks. Thank once again.