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Transcript of Trigonometry
Decide how to solve for its other angles/sides
Apply the law of sines to the situation The Problem In some triangles, where 2 sides and an angle are given, where the angle is not between the two sides (SSA) there is more than one possible triangle to solve for. The black values represent given information. Why does this problem arise? It is because of the nature of the inverse sine operation In these certain cases, there are alwas 2 possibilities for the angle, where one possibility is the supplement of the other. We can also put this into a more geometric perspective. If the side opposite the given angle is shorter than the other given side, but longer than a hypothetical altitude drawn from the endpoint of the given side, then there are 2 possible angles. In other words, when a<b and a>bsinA A, B, and C are the angles of a triangle
while a, b, and c are the opposite sides
to their corresponding angles Using the Law of Sines, one can make an equation where the sine of the given angle over the given side equals the sine of the unknown angle over the sine of the other given side. However, when the equation is simplified, the result for the unknown angle is an arcsin expression. And in yet another perspective, it is when arcsin(b[sin(A)/a) has 2 solutions in the range [0,180] or [0,π] Trigonometry:
The Law of Sines Sample Problem: In a triangle ABC, given that angle A has a measure of 50 degrees and angle B has a measure of 65 degrees, while side a has a length of twelve, find the rest of the values of the triangle here is a link demonstrating the possibilities of the ambiguous case:
http://www.marckerschner.com/teaching-resources/law-of-sines-ambiguous-case/ This interactive animation helps give a visual idea of how the ambiguous case works, and under which conditions it appears.