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Download Trigonometry Summary AND `The AMBIGUOUS Case`... Ambiguous
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Untitled.notebook March 29, 2016 Trigonometry Summary AND 'The AMBIGUOUS Case'... Ambiguous Case 1 Untitled.notebook Notes Ambiguous Case.pdf March 29, 2016 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) 2 Untitled.notebook MUST MEMORIZE THESE March 29, 2016 Criteria for the Ambiguous Case... • Must be given SSA • Given angle is acute b • a < b a *** If ALL 3 criteria are met, then... CALCULATE THE ALTITUDE NOTES alt = b sin A A B CASE 1: a < altitude; there is NO SOLUTION IN ORDER TO KNOW AMBIGUOUS CASE 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) Back to the Warm-Up... 1. Determine the measure of the obtuse angle B: 3 Untitled.notebook March 29, 2016 4 Untitled.notebook March 29, 2016 Example 2: Solve the triangle ABC if a = 10, b = 12 and angle A = 72o. 5 Untitled.notebook March 29, 2016 Example 3: B A C A B 6 Untitled.notebook March 29, 2016 7 Untitled.notebook March 29, 2016 HOMEWORK... Worksheet Ambiguous Case.pdf Do questions #1, 2, 4, 5 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) 8 Attachments Notes Ambiguous Case.pdf Worksheet Ambiguous Case.pdf
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