The past few days we have talked about the Law of Sines, Law of Cosines, and the Side Side Angle (SSA) ambiguity. SSA is considered ambiguous because there can be more than one triangle created with the given information. You can't simply apply the Law of Sines with the given information, because you must first find the altitude of the triangle, and then further decide if there is zero, one, or two solutions. If the side across from the given angle is larger than the altitude, there will be two solutions, if it is equal to the amplitude, there will be one solution, and if it is shorter than the amplitude, there will be no solutions. There is an example in the gallery below.
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The graph above is an equation that displays how many hours of sunlight (y value) are in a day for each month (x value) for Yuma. If Cress wants to move to Yuma, but only if there is sunlight for at least half the day for half the year, this means through x values 1-12, at least 6 of those must have y values greater than 12. For months 1, 2, 9, 10, 11, and 12, the y values are less than 12, and for months 3, 4, 5, 6, 7, 8, and 9, the y values are greater than 12. This means that there is sunlight for at least half the day for at least half the year, and Cress will be satisfied with the sunlight. |