# Law of sines--ambiguous problem

Discussion in 'General Math' started by hgl, Jul 9, 2004.

1. ### hglGuest

a=65,c=62,h=63.5,C=78 degrees

what is A?

If there is no solution, why?

hgl, Jul 9, 2004

2. ### David MoranGuest

By the Law of Sines,

65/sin A=62/sin78, which is the same as 62sin A=65sin78 therefore sin
A=1.0255. Since the range of sine is -1 to 1, there's no solution.

Dave

David Moran, Jul 9, 2004

3. ### Andrew B. ParkGuest

Do you mean ambiguous, or "overdetermined"? If the information given
here were to be set down into equations... you will have more
information than you need to define a triangle--and if any of your
information turns out to be... well, inconsistent, then you don't have
a solution that can satisfy all the equations (it's kind of like
asking for a right triangle with an obtuse angle).

Anyway, the way I understand it here, you have lengths of all three
sides, which is sufficient to define a triangle. All you need to do is
to calculate the triangle (which is quite trivial--a machine
(specifically, my TI-83 calculator which has a triangle-solving
program I made years ago) can do it), and see if the angle is
consistent with the result you get.

Andrew B. Park, Jul 9, 2004