It's stated that the dots mean the side a can swing freely, but in example (b) I think it can't move since the side b and the angle A is immobile.

Length of b and size of angle A remain constant, but in all cases side "a" is free to swing.
I can't read what is written in red??
 
Harry_the_cat said:
Length of b and size of angle A remain constant, but in all cases side "a" is free to swing.
I can't read what is written in red??
Click to expand...
it says if a moves, the angle B won't be 90 degrees anymore. I can't understand how it can move, a and h are equal so I thought a is the shortest line that goes down from C to ground. If a moves even one degrees, it won't meet the ground anymore and there won't be a triangle
 
stabatpatriae said:
it says if a moves, the angle B won't be 90 degrees anymore. I can't understand how it can move, a and h are equal so I thought a is the shortest line that goes down from C to ground. If a moves even one degrees, it won't meet the ground anymore and there won't be a triangle
Click to expand...
Please post more details. What's the context?
In my opinion the idea is that side a can rotate around the point C. The question is, where does a intersect the horizontal dashed line (point B). Depending on a's length there are 3 possibilities:
No solutions.
One solution.
2 solutions.
 
Harry_the_cat said:
Have you learnt any trigonometry yet? For example, do you know what the sine ratio is? If you have, I can explain it using those terms.
Click to expand...
Ok I can see a reference to sine on your diagram, so I'll try to explain using an example.
You should know that sin 30° = 1/2.
Draw a horizontal line from point A, and draw a 2 inch line at 30° to it to point C, to look like the diagrams you have shown.
If you drop a perpendicular to the horizontal line, like in the second diagram, the length of this perpendicular will be 1 inch. (That's because sin 30°=1/2.) So, if you are asked to draw a triangle with A=30°, b=2 inches and a=1 inch, there is only one possible triangle you can draw.
Now, if A=30°, b=2 and a<1, you could not draw a triangle because a isn't long enough to reach the other side. (See your first diagram)
Also, if A=30° , b=2 and a>1, there are 2 possible triangles you can draw (see your third diagram). One will have an acute angle at B and the other one will have an obtuse angle at B.
(This is leading you into what is known as the "ambiguous case" of the sine rule.)
 
Harry_the_cat said:
Ok I can see a reference to sine on your diagram, so I'll try to explain using an example.
You should know that sin 30° = 1/2.
Draw a horizontal line from point A, and draw a 2 inch line at 30° to it to point C, to look like the diagrams you have shown.
If you drop a perpendicular to the horizontal line, like in the second diagram, the length of this perpendicular will be 1 inch. (That's because sin 30°=1/2.) So, if you are asked to draw a triangle with A=30°, b=2 inches and a=1 inch, there is only one possible triangle you can draw.
Now, if A=30°, b=2 and a<1, you could not draw a triangle because a isn't long enough to reach the other side. (See your first diagram)
Also, if A=30° , b=2 and a>1, there are 2 possible triangles you can draw (see your third diagram). One will have an acute angle at B and the other one will have an obtuse angle at B.
(This is leading you into what is known as the "ambiguous case" of the sine rule.)
Click to expand...
thank you
 
lev888 said:
Please post more details. What's the context?
In my opinion the idea is that side a can rotate around the point C. The question is, where does a intersect the horizontal dashed line (point B). Depending on a's length there are 3 possibilities:
No solutions.
One solution.
2 solutions.
Click to expand...
I got it, but thanks
 
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