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Side‐Angle Relationships in Acute and Obtuse Triangles
Oblique triangles a triangle that does not contain a 900 angle.
Acute Triangle a triangle which all angles are less than 900.
Obtuse triangles in which one of the angles is an obtuse angle. Have one angle that is greater than 900 and but less than 1800.
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WARM UP
A
BC
18 m 105o
53o
Find side length a, round to tenths place
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OR
Use this if solving for a side length Use this if solving for an angle
Solving for an Angle using the Sine Law
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Example 1: Finding an unknown angle
Consider the triangle below. Find ∠f. Round to nearest degree.
ALWAYS check for ambiguous case with SSA when solving for an angle with the Law of Sines. There maybe one or more solutions or even no solution when solving for the triangle. You will not be reminded to check in the question on test/exam.
in order to have 2 triangles, Angle given in question and supplementary angle must have sum less than 180o ,
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x y00
300
600900120015001800
2100
240027003000
33003600
Complete the table of values if y = sin(x).
Exploring Primary Trig Ratios for Obtuse and Acute Angles
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Look at your table of values, between 0° and 180°, for which two angles does Sin(x) = 0.5?
What do these two angles sum to?
Look at your table of values, between 0° and 180°, for which two angles does Sin(x) = 0.866?
What do these two angles sum to?
Find the value of the following,
Sin 20° = ______ Sin 45° = ______ Sin 10° =____
Sin 160° = _____ Sin 135° = _____ Sin 170° =____
What rule or property do you see happening in the above three examples?
Find all angles, A, between 0° and 180° for which the following is true
Sin A = 0.66913 Sin A = 0.90631 Sin A = 0.819152
IMPORTANT!!!!!!!!
Supplementaryangles have same
trig ratio
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Section 4.3 - The Ambiguous Case of the Sine Law
Ambiguous Case of the Sine Law: a situation in which 2 triangles can be drawn. This may occur when the given measurements are the lengths of 2 sides and the measure of an angle that is not contained by the 2 sides (SSA)By definition the word ambiguous means open to two or more interpretations. Such is the case for certain solutions when working with the LAW OF SINES
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Example 2: What is the measure of the angle opposite of the side that has a length of 20?
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Example 2: What is the measure of the angle opposite of the side that has a length of 20?
33o 89o
given
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http://www.mathwarehouse.com/trigonometry/lawofsines/ambiguouscaseoflawofsines.php
Interactive Demonstration of the Ambiguous Case
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Example 1: Finding an unknown angle
Consider the triangle below. Find ∠F and ∠E. Round to nearest degree.
ALWAYS check for ambiguous case with SSA when solving for an angle with the Law of Sines. There maybe one or more solutions or even no solution when solving for the triangle. You will not be reminded to check in the question on test/exam.
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Example 3: How to find unknown angles
What is the measurement of angle B?
arepossible
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Example 4: Finding an unknown angle: What is the measurement of angle c
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Example 4: Finding an unknown angle: What is the measurement of angle c
