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Untitled.notebook March 28, 2017 Warm Up 1. Determine the measure of the obtuse angle B: 1 Untitled.notebook March 28, 2017 2 Untitled.notebook March 28, 2017 3 Untitled.notebook March 28, 2017 4 Untitled.notebook March 28, 2017 Trigonometry Summary AND 'The AMBIGUOUS Case'... Ambiguous Case 5 Untitled.notebook Notes Ambiguous Case.pdf March 28, 2017 Criteria for the Ambiguous Case... • Must be given SSA • Given angle is acute • a < b b a *** If ALL 3 criteria are met, then... CALCULATE THE ALTITUDE alt = b sin A A B CASE 1: a < altitude; there is NO SOLUTION CASE 2: a = altitude; there is ONE SOLUTION [Right Triangle] CASE 3: a >altitude; this is the 'AMBIGUOUS CASE'...TWO SOLUTIONS 1) Acute Triangle (angle, θ, is found with Law of Sines) 2) Obtuse Triangle (angle is 180ο θ) 6 Untitled.notebook MUST MEMORIZE March 28, 2017 Criteria for the Ambiguous Case... • Must be given SSA • Given angle is acute THESE b • a < b a *** If ALL 3 criteria are met, then... NOTES IN ORDER TO KNOW CALCULATE THE ALTITUDE alt = b sin A A B CASE 1: a < altitude; there is NO SOLUTION CASE 2: a = altitude; there is ONE SOLUTION [Right Triangle] CASE 3: a >altitude; this is the 'AMBIGUOUS CASE'...TWO SOLUTIONS 1) Acute Triangle (angle, θ, is found with Law of Sines) 2) Obtuse Triangle (angle is 180ο θ) AMBIGUOUS CASE Back to the Warm-Up... 1. Determine the measure of the obtuse angle B: 7 Untitled.notebook March 28, 2017 8 Untitled.notebook March 28, 2017 Example 2: Solve the triangle ABC if a = 10, b = 12 and angle A = 72o. 9 Untitled.notebook March 28, 2017 Example 3: B A C A B 10 Untitled.notebook March 28, 2017 HOMEWORK... Worksheet Ambiguous Case.pdf Do questions #1, 2 & 4 MEMORIZE!!! Criteria for the Ambiguous Case... • Must be given SSA • Given angle is acute • a < b b a *** If ALL 3 criteria are met, then... CALCULATE THE ALTITUDE alt = b sin A A B CASE 1: a < altitude; there is NO SOLUTION CASE 2: a = altitude; there is ONE SOLUTION [Right Triangle] CASE 3: a >altitude; this is the 'AMBIGUOUS CASE'...TWO SOLUTIONS 1) Acute Triangle (angle, θ, is found with Law of Sines) 2) Obtuse Triangle (angle is 180ο θ) 11 Attachments Notes Ambiguous Case.pdf Worksheet Ambiguous Case.pdf
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