Thank you for your time!

With regards and happy new year!

- Thread starter jmrg2992
- Start date

Thank you for your time!

With regards and happy new year!

I have done it again with the unrounded values, but there wasn't a significant change in the results.When you calculated angle A, you rounded it to two decimal places. When calculating sin(B), you should use the unrounded value you obtained for A.

So this is one special case where ambiguous results might happen?In general the law of cosines gives unambiguous results, since arccos is single valued for angles 0 to 180. Arcsin is double valued over this range.

But theorethically once we have an angle like in this conditions knowing the sides, the results should be equal if I mix the cosine and the sine law, right? Well unless we can have two values for one single angle like this exercise.In general, one doesn't have the luxury of being able to choose which method to use.

Also thanks to everyone for the answers !!! I really appreciate it !

Potential ambiguity arises when the sine of an angle is used to determine the angle, but it's usually easy to determine the correct value. Some textbooks don't cover this in detail.So this is one special case where ambiguous results might happen?

In the example originally posted, the cosine method needs to be applied first, as no angle is known initially. Having found that angle A, say, is arccos(203/220), which is approximately 22.672 degrees, one can choose to find sin(B), which turns out to be 0.8479976415..., and arcsin of that is 57.994545... degrees. If angle B had that value, angle C would be obtuse, which is impossible, as AB isn't the longest side of the triangle (if a triangle has an obtuse angle, the side opposite that angle must be longer than each of the other two sides, because the obtuse angle must be greater than each of the other two angles). Hence angle B = 180° - 57.994545... degrees = 122.00545... degrees. If that explanation is considered too cumbersome, one can use the cosine method instead to show that cos(B) = -0.53 exactly, etc.

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