So I'm in 10th grade taking my regents and finals and I came across a peculiar problem on the NYS Regents for Algebra 2 Trig
Off the top of my head, here it goes...
2 forces act upon a single point, one force being 40 pounds, and the other being 28 pounds, creating an angle of 65 degress. Find the resultant length to the nearest pound. Using this answer, find the angle measure between the smaller force and the resultant, to the nearest degree.
Ok, so I drew a parallelogram with one side of 40 and another of 28, found the supplement angle to be 115 and used the law of cosines to get 58 as my Resultant length.
Then I used the law of sines to find the smaller force and resultant angle, and I got the angle to be 38.32..., rounded to 38. BOOM! Done.
However, knowing me, I always do my problems at least 2 different ways, check through my test and I try finding that same angle by using the law of cosines instead. Sure enough, I got roughly the same answer, 38.6....rounded to..wait..39?
I am freaking out. I call over my teacher and I explain to him/her what I have done, after a brief talk, they walk over to the front of the gymnasium and converse with the other teachers. One teacher comes over to me and says "Just circle both answers. We're going to find out what is wrong" So I do what they say and the test goes on.
My question for you math lovers, can you (1) Explain to me what was going and (2) What is the true answer to this question. Even stranger, I went outside after the test and sure enough, I hear mixed answers, 38, 39, etc. I go up to my teacher and ask them "Were there really two answers to that last question" and he told me "Theoretically yes". Can anyone help me with this?
Off the top of my head, here it goes...
2 forces act upon a single point, one force being 40 pounds, and the other being 28 pounds, creating an angle of 65 degress. Find the resultant length to the nearest pound. Using this answer, find the angle measure between the smaller force and the resultant, to the nearest degree.
Ok, so I drew a parallelogram with one side of 40 and another of 28, found the supplement angle to be 115 and used the law of cosines to get 58 as my Resultant length.
Then I used the law of sines to find the smaller force and resultant angle, and I got the angle to be 38.32..., rounded to 38. BOOM! Done.
However, knowing me, I always do my problems at least 2 different ways, check through my test and I try finding that same angle by using the law of cosines instead. Sure enough, I got roughly the same answer, 38.6....rounded to..wait..39?
I am freaking out. I call over my teacher and I explain to him/her what I have done, after a brief talk, they walk over to the front of the gymnasium and converse with the other teachers. One teacher comes over to me and says "Just circle both answers. We're going to find out what is wrong" So I do what they say and the test goes on.
My question for you math lovers, can you (1) Explain to me what was going and (2) What is the true answer to this question. Even stranger, I went outside after the test and sure enough, I hear mixed answers, 38, 39, etc. I go up to my teacher and ask them "Were there really two answers to that last question" and he told me "Theoretically yes". Can anyone help me with this?