G
Guest
Guest
yep, the subject asks all, so how do you know if a triangle is amibuous?????????????????????????????????//
Thanks for the help,
Anna
Thanks for the help,
Anna
- Joined
- Apr 12, 2005
- Messages
- 11,339
First of all, is MUST be a case of knowing two sides and an angle NOT included. If that is what you have, there are only five ways for it to fall out if the known angle is acute:
Orient your supposed triangle so that the unknown side is the base.
Label angle A, the known angle.
Label angle C, the apex angle.
Label side b, the side between A and C.
Draw the base, c, of unknown length from Angle A, horizontal and long enough to get well under Angle C.
Draw a fake side 'a', opposite angle A, down from Angle C, perpendicular to side c, the base.
Mark the right angle just created.
Lable the length of this fake side, side 'a', by its length, b*sin(A) -- That's the length if is a Right triangle.
1) a = b*sin(A) ==> Right Triangle - 'a' exactly meets the base in one place.
2) a < b*sin(A) ==> No Triangle - 'a' isn't long enough to reach the base.
3) a = b ==> One Triangle - An isosceles triangle.
4) a > b ==> One Triangle - If you swing 'a' around, it won't hit anything on the same side of angle A.
5) b*sin(A) < a < b ==> Here is your ambiguous case.
So,
1) 'A' is known angle
2) 'a' is the known side opposite angle A
3) 'b' is the other known side.
4) Calculate b*sin(A) and see where 'a' falls.
In a different order, increasing the length of 'a':
1) a < b*sin(A) < b ==> No Triangle
2) a = b*sin(A) < b ==> One Right Triangle
3) b*sin(A) < a < b ==> Ambiguous Case
4) b*sin(A) < a = b ==> One Isosceles Tiangle
5) b*sin(A) < b < a ==> One Triangle
Orient your supposed triangle so that the unknown side is the base.
Label angle A, the known angle.
Label angle C, the apex angle.
Label side b, the side between A and C.
Draw the base, c, of unknown length from Angle A, horizontal and long enough to get well under Angle C.
Draw a fake side 'a', opposite angle A, down from Angle C, perpendicular to side c, the base.
Mark the right angle just created.
Lable the length of this fake side, side 'a', by its length, b*sin(A) -- That's the length if is a Right triangle.
1) a = b*sin(A) ==> Right Triangle - 'a' exactly meets the base in one place.
2) a < b*sin(A) ==> No Triangle - 'a' isn't long enough to reach the base.
3) a = b ==> One Triangle - An isosceles triangle.
4) a > b ==> One Triangle - If you swing 'a' around, it won't hit anything on the same side of angle A.
5) b*sin(A) < a < b ==> Here is your ambiguous case.
So,
1) 'A' is known angle
2) 'a' is the known side opposite angle A
3) 'b' is the other known side.
4) Calculate b*sin(A) and see where 'a' falls.
In a different order, increasing the length of 'a':
1) a < b*sin(A) < b ==> No Triangle
2) a = b*sin(A) < b ==> One Right Triangle
3) b*sin(A) < a < b ==> Ambiguous Case
4) b*sin(A) < a = b ==> One Isosceles Tiangle
5) b*sin(A) < b < a ==> One Triangle
G
Guest
Guest
sry guys, I spelt it wrong. It's actually called Ambiguous.
FOr ex. A triangle ABC is shown. <A= 44.3 degress, a=11.5m, and b= 7.7 m.
My teacher said to see if an unknown angle you have to find is greater than the given angle. If the unknown angle is greater, then it's an ambiguous triangle, but in this Example I found in the text book, her theory is wrong?
They got for <B= 27.9 degrees and <C= 107.8 degrees <--that angle C is larger than the given angle <A= 44.3 degrees.
BUT the book says there's only one solution..so I'm confused.
HELP
FOr ex. A triangle ABC is shown. <A= 44.3 degress, a=11.5m, and b= 7.7 m.
My teacher said to see if an unknown angle you have to find is greater than the given angle. If the unknown angle is greater, then it's an ambiguous triangle, but in this Example I found in the text book, her theory is wrong?
They got for <B= 27.9 degrees and <C= 107.8 degrees <--that angle C is larger than the given angle <A= 44.3 degrees.
BUT the book says there's only one solution..so I'm confused.
HELP
G
Guest
Guest
ya I know the meaning of ambiguous denis..but anyways, I found out how you can tell if it is or isn't now. From the given angle, if the opposite side is SMALLER than the adjacent side, then the triangle is ambiguous.
THANKS for the help and your time,
Anna
THANKS for the help and your time,
Anna
anna said:
...the bird is the word, the word, the word is probably "obtuse"...
AGAIN: solving a triangle (not the triangle) is AMBIGUOUS if the
information given is NOT SUFFICIENT to result in a UNIQUE triangle:
don't keep arguing: instead, get your teacher on this board: we'll
fix his/her clock!
Hmmm; just reminded of this ad: if your clock don't tick, tock to us
- Joined
- Apr 12, 2005
- Messages
- 11,339
Calculate b*sin(A) = 7.7 m * sin(44.3°) = 5.378 manna said:
1) a < b*sin(A) < b ==> No Triangle
2) a = b*sin(A) < b ==> One Right Triangle
3) b*sin(A) < a < b ==> Ambiguous Case
4) b*sin(A) < a = b ==> One Isosceles Tiangle
5) b*sin(A) < b < a ==> One Triangle
It's an important list.