Precalculus MATH 1730
pellissippi state community college
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This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1730 at pellissippi state community college taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/232970/math-1730-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.
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Date Created: 11/01/15
USING TRIGONOMETRY SOLVING A TRIANGLE Solving a triangle means nding the sizes of all angles and sides To get the most accurate results use given information whenever possible and do not approximate until the nal step I Given two angles and one side ASA or AAS A Find third angle by subtracting sum of known angles from 180 B Use Law of Sines to nd unknown sides ll Given two sides and an angle opposite one of the known sides SSA A Use Law of Sines to nd angle opposite other known side lfthe sine of the angle is greater than one then NO triangle can be constructed with given parts B Subtract the angle found in Part A from 180 to get second possibility One of the angles found in Parts A and B will be obtuse Add obtuse angle to given angle 1 If resulting sum is greater than or equal to 180 discard the obtuse angle as an option Use Law of Sines or Law of Cosines to nd third side 2 If resulting sum is less than 180 do two separate calculations as there are two different triangles possible Use Law of Sines or Law of Cosines to nd each third side lll Given two sides and included angle SAS A Use Law of Cosines to nd third side B Use Law of Sines or Law of Cosines to find smaller of two unknown angles This angle will be opposite the shorter side This angle will always be acute thus avoiding ambiguity Subtract sum of the two angles from 180 to nd third angle 0 IV Given three sides SSS A Use Law of Cosines to nd largest angle opposite largest side Finding this angle rst guarantees that remaining two angles will be acute no ambiguity exists B Use Law of Sines or Law of Cosines to nd a second angle Subtract sum of the two angles from 180 to nd third angle 0 V Given three angles AAA not enough information to determine a unique triangle
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