M1410601Chart - OR Find 2nd angle using Law of Sines Find...

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SECTIONS 6.1-6.2 SOLVING A TRIANGLE (T) AAA Can’t solve: Family of similar triangles (if angle sum = 180 o ) Assume that any given angle measure (or the sum of any two given angle measure lies in the interval (0 o , 180 o ). Otherwise, there is no such T. "Find 3rd angle": Subtract the other two angle measures from 180 o . 2 angles, 1 side (SAA, ASA) Find 3rd angle Use Law of Sines to find 2nd, 3rd sides SSA (Two sides and a non-included angle) AMBIGUOUS CASE!! (Possibly 2 triangles) Find candidates for 2nd angle using Law of Sines If get a sin value > 1 .... No such T exists!! sin -1 result Find 3rd angle Find 3rd side supplementary angle Find 3rd angle Find 3rd side If angle < 0 o , KILL THIS CASE!! There is only one triangle . CONTINUED
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FINDING THE AREA OF A TRIANGLE (T) SAS (Two sides and their included angle) Use Law of Cosines to find 3rd side
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Unformatted text preview: OR Find 2nd angle using Law of Sines . Find the smaller of the two remaining angles (compare their opposite sides to see which is smaller); this angle must be acute. Find 2nd angle using Law of Cosines Find 3rd angle SSS Find an angle using Law of Cosines . Find the largest angle (it faces the longest side) if you intend to use the Law of Sines later. The other two angles must be acute. Find a 2nd angle using Law of Cosines . Find a 2nd angle using Law of Sines . Find 3rd angle Find 3rd angle SAS Use (for example) Area = SSS Otherwise. .. If the Triangle Inequality fails. .. No such T exists!! Use Heron’s Formula If the Triangle Inequality fails. .. No such T exists!! Otherwise. .. Find 3rd angle 1 2 ab sin C...
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