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6.1 Law of Sines. +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases. Oblique Triangles. A is acute. A is obtuse. B. B. c. a. a. c. A. C. b. C. A. b. Solving Oblique Triangles. - PowerPoint PPT Presentation
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6.1 Law of Sines+Be able to apply law of sines to find missing sides and
angles+Be able to determine ambiguous cases
Oblique TrianglesA is acute A is obtuse
A
a
B
b C
c
A
B
C
a
b
c
Solving Oblique Triangles
• To solve oblique triangles you need one of the following cases• 2 angles and any side (AAS or ASA)• 2 sides and the angle opposite one of them
(SSA)• 3 sides (SSS)• 2 sides and their included angle (SAS)
Law of Sines
• If ABC is a triangle with sides a, b, and c, then
Example
• Find the missing sides and angles given the following information• C = 102.30
• B = 28.70
• b = 27.4 ft
Word Problem
• A pole tilts towards the sun at an 80 angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 430. How tall is the pole?
Ambiguous Cases (SSA)(h = bsinA)
• A is acute
• a < h
• no triangles
• A is acute
• a = h
• 1 triangle
A
a
hb
A
b ah
More Cases• A is acute
• a > b
• 1 triangle
• A is acute
• h < a < b
• 2 triangles
A
b ah
A
b ha a
More Cases• A is obtuse
• a < b
• no triangles
• A is obtuse
• a > b
• 1 triangle
A
a
b
A
ba
Example
• Find the missing sides and angles of the triangle given the following information• a = 22 in• b = 12 in • A = 420
Determine how many triangles there would be?
1) A = 620 , a = 10, b = 12
2) A = 980 , a = 10, b = 3
3) A = 540 , a = 7, b = 10
Finding two solutions
• Find two triangles for which a = 12, b = 31, and A = 20.50
Example
• Find the missing sides and angles for the following information• a = 29• b = 46• A = 310
Using Sine To Find Area• Area of an Oblique Triangle
Find the Area of the Triangle
• Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102o.
Word Problem• The course for a boat race
starts at point A and proceeds in the direction S 52o W to point B, then in the direction S 40o E to point C, and finally back to point A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.
