Ambiguous Triangles

Hi. Paul here. ;P Today Mr. P discussed about "Ambiguous Triangles". We constructed triangles using the given measurements. We also proved using algebraic method if a triangle is possible or not.

We used Sine Law...

...to prove if a triangle is possible or not. It's just basically plugging in the given measurements and solve for the missing variable.

Angle A = Sin30

Side b = 10

Side a = any number..

This is our examples today and I wanna use this one to explain this.

If you notice, side a is the one that changes in the examples given. Sin30*10 is always 5. It's easier to prove if the triangle given is possible or not just by dividing 5 to side a and if it is more than one then it's not possible.

You can also get two answers but it depends. If you'll have an answer of related angle, be sure that the sum of the angles of the triangle add up to 180 degrees because remember that there is still angle C.

Mr. P showed us 4 cases today for Acute Triangles but I'm gonna give one more case.

Case 1 = side a is too short

Case 2 = side a is just exact to form 90 degrees angle

Case 3 = side a is not too long not too short that it can form two types of triangles

Case 4 = side a is exactly the same as side b that it forms isosceles triangle ***

Case 5 = side a is long that it can form only one type of triangle

Well that's it. You just have to use the sine law in this case and check if the angles are equal to 180 degrees and you can answer the question even without drawing the triangle. ;D Remember, Sine Law, Plug in, Add Sum of the angles and check for 180. ;) Test coming up! Goodluck to all of us! :D