Unformatted text preview: C to AB has height h = b sin A . As we can see in Figure 2.1.3(a)-(c), there is no solution when a < h (this was the case in Example 2.3); there is exactly one solution - namely, a right triangle - when a = h ; and there are two solutions when h < a < b (as was the case in Example 2.2). When a ≥ b there is only one solution, even though it appears from Figure 2.1.3(d) that there may be two solutions, since the dashed arc intersects the horizontal line at two points. However, the point of intersection to the left of A in Figure 2.1.3(d) can not be used to determine B , since that would make A an obtuse angle, and we assumed that A was acute. If A is not acute (i.e. A is obtuse or a right angle), then the situation is simpler: there is no solution if a ≤ b , and there is exactly one solution if a > b (see Figure 2.1.4)....
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- Fall '11
- Calculus, Law of sines, ambiguous case