My sense is that this mistake isn’t as interesting as the rest, but it’s a pretty common one that I see in Trigonometry. The question is, what sort of activity would help this student out?

4 replies on “Trigonometry – Find the missing angle”

Looks like this student has some confusion with the law of sines and is using the angle measure rather than the sine of the angle measure. The other probelm I see is the way the student has drawn the triangle (they probably just drew it before writing down lengths), but I wonder if the student could really compare 3 and 3sqrt2 and come to the realization that 3sqrt2 is about 40% bigger than the other side. I’m wondering if the the radical made the two lengths hard for the student to compare (not that a comparison is necessary to solve this problem, but I think it might be helpful in checking answers. What would help this student out? I think some practice with law of sines, and in particular understanding the difference between the sine of the angle and the angle itself.

Notice also the law of cosines scribbled on the right. Apparently the student wasn’t even particularly confident in the choice of law of sines.I’m always a little bit conflicted giving kids the law of sines. This year I had one student who just drew an altitude every time and solved the triangle without the shortcut.

As for your question, I think in an ideal world I would go through this sequence (stopping when the student “gets it”): Give him the correct answer and ask him to generate it (hoping he will find his mistake that way), re-deriving the formula with his help, and showing him the worked out solution step-by-step so that he can see the formula in action. This probably needs to be followed up by a discussion of when to use which formula.2 things I noticed that are off task:1. The student didn’t take advantage of the special right triangle formula when he could have. However, most of my students fail to use that once they have been exposed to trig.2. The student also has trouble with sqrt(2) since in his abortive attempt to use the LoC, he gets 6 for C^2.

Is anyone else bothered by the student writing two versions of the LOC? I have seen this in books as well, where they list the formula three times. I do teach LOS, but I am kinda with Michael on that. LOS seems like a better problem (come up with a formula…) than a tool.

## 4 replies on “Trigonometry – Find the missing angle”

Looks like this student has some confusion with the law of sines and is using the angle measure rather than the sine of the angle measure. The other probelm I see is the way the student has drawn the triangle (they probably just drew it before writing down lengths), but I wonder if the student could really compare 3 and 3sqrt2 and come to the realization that 3sqrt2 is about 40% bigger than the other side. I’m wondering if the the radical made the two lengths hard for the student to compare (not that a comparison is necessary to solve this problem, but I think it might be helpful in checking answers. What would help this student out? I think some practice with law of sines, and in particular understanding the difference between the sine of the angle and the angle itself.

Notice also the law of cosines scribbled on the right. Apparently the student wasn’t even particularly confident in the choice of law of sines.I’m always a little bit conflicted giving kids the law of sines. This year I had one student who just drew an altitude every time and solved the triangle without the shortcut.

As for your question, I think in an ideal world I would go through this sequence (stopping when the student “gets it”): Give him the correct answer and ask him to generate it (hoping he will find his mistake that way), re-deriving the formula with his help, and showing him the worked out solution step-by-step so that he can see the formula in action. This probably needs to be followed up by a discussion of when to use which formula.2 things I noticed that are off task:1. The student didn’t take advantage of the special right triangle formula when he could have. However, most of my students fail to use that once they have been exposed to trig.2. The student also has trouble with sqrt(2) since in his abortive attempt to use the LoC, he gets 6 for C^2.

Is anyone else bothered by the student writing two versions of the LOC? I have seen this in books as well, where they list the formula three times. I do teach LOS, but I am kinda with Michael on that. LOS seems like a better problem (come up with a formula…) than a tool.