The sine rule still holds - what you can do is "pivot" the side of length 7 clockwise around the top vertex, maintaining its length, and it will again meet the base and this time theta will be 115 degrees. None of the other stipulated angles/sides are affected. This same ambiguity is why SSA is insufficient to show congruence, because you can have two cases which satisfy the criteria and which are geometrically different shapes.
I thought the first step in solving an SSA triangle (ambiguous case), is to find the altitude from the vertex between the 2 given side lengths to the opposite side - in order to determine if your solution will be 1, 2, or 0 triangles.
There are multiple ways of solving it, or proving that you don't have enough information to solve it. There isn't necessarily a single first step, that is the only possible first step.
I believe sine has two solution because it (y) can be positive twice. in quadrant I and in II. Position 65 in I is 180-65 in II, which is 115. Something like that.
You need at minimum, three pieces of information to define a triangle. 2 angles and a side (AAS / ASA), 2 sides and the angle between them (SAS), all 3 sides (SSS), or knowledge that it is a right triangle and any other two pieces of data. If you have all 6 pieces of information, you've more than fully defined the triangle. The ASS congruence property doesn't exist because of the ambiguous case, where the side opposite the angle has two possible touchdown points. You could get a special case of the ASS triangle, if the opposite side to the given angle touches down at exactly one point. Or you could get no solution.
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I thought the sin(45) is root 2 over 2 not 1 on root 2 as stated. LOL never mind. they are the same if multiplied by root 2 over root 2.
pre calc has my brain fries thanks for the help
The sine rule still holds - what you can do is "pivot" the side of length 7 clockwise around the top vertex, maintaining its length, and it will again meet the base and this time theta will be 115 degrees. None of the other stipulated angles/sides are affected.
This same ambiguity is why SSA is insufficient to show congruence, because you can have two cases which satisfy the criteria and which are geometrically different shapes.
I was struggling to pivot correctly in my head thinking hang on Why isn't this working?!...but I forgot to use the base as the reference point. Thanks
Hello sir
Sir could you explain at 5:00 that if the obtuse angle is used is te length opposite to it 9?
I thought the first step in solving an SSA triangle (ambiguous case), is to find the altitude from the vertex between the 2 given side lengths to the opposite side - in order to determine if your solution will be 1, 2, or 0 triangles.
There are multiple ways of solving it, or proving that you don't have enough information to solve it. There isn't necessarily a single first step, that is the only possible first step.
How did the students know the other possible solution was 115
The other solution is 180-theta
I believe sine has two solution because it (y) can be positive twice. in quadrant I and in II. Position 65 in I is 180-65 in II, which is 115. Something like that.
Because range of internal angle is zero to 180degree and there is two angle between 0 to 180 for one positive value of sine
Because if 65° was one soln then the other will be (180 - 65° ) {this is based on periodicity of sin graph }
sin(x) = sin(180 - x)
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how did you get 9/7root2 from sin45/7 and times 9 (1:38)
(9 times 1/root2 )/7
@@eduardjosephpalmiano5288 mind going more in depth?
@@nashhenley7432 sin45 is equal to 1/root2, then you have 7 in the denominator, so it becomes 1/7root2. lastly, cross multiply 9, giving you 9/7root2
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hi Mr. Eddie, if all the 3 angles and the value of three sides are given, can we still form the ambiguous case? can it be exist?
You need at minimum, three pieces of information to define a triangle. 2 angles and a side (AAS / ASA), 2 sides and the angle between them (SAS), all 3 sides (SSS), or knowledge that it is a right triangle and any other two pieces of data. If you have all 6 pieces of information, you've more than fully defined the triangle.
The ASS congruence property doesn't exist because of the ambiguous case, where the side opposite the angle has two possible touchdown points. You could get a special case of the ASS triangle, if the opposite side to the given angle touches down at exactly one point. Or you could get no solution.
How do you know that the other side is not bigger?
Aneeqa you can tell by looking at the pic
Jipsey21
What is it's not to scale oWo
how did you get 115 degrees
Sin theter= sin (180degrees-theter)
4:27 why no 3 solutions?
JUmp to10:06, he wrote it down
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