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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.

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6 1 law of sines

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
Oblique Triangles

A is acute

A is obtuse

B

B

c

a

a

c

A

C

b

C

A

b


Solving oblique triangles
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
Law of Sines

  • If ABC is a triangle with sides a, b, and c, then


Example
Example

  • Find the missing sides and angles given the following information

    • C = 102.30

    • B = 28.70

    • b = 27.4 ft


Word problem
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
Ambiguous Cases (SSA)(h = bsinA)

  • A is acute

  • a < h

  • no triangles

  • A is acute

  • a = h

  • 1 triangle

a

b

b

h

a

h

A

A


More cases
More Cases

  • A is acute

  • a > b

  • 1 triangle

  • A is acute

  • h < a < b

  • 2 triangles

b

b

a

a

a

h

h

A

A


More cases1
More Cases

  • A is obtuse

  • a < b

  • no triangles

  • A is obtuse

  • a > b

  • 1 triangle

a

a

b

b

A

A


Example1
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
Determine how many triangles there would be?

  • A = 620 , a = 10, b = 12

  • A = 980 , a = 10, b = 3

  • A = 540 , a = 7, b = 10


Finding two solutions
Finding two solutions

  • Find two triangles for which a = 12, b = 31, and A = 20.50


Example2
Example

  • Find the missing sides and angles for the following information

    • a = 29

    • b = 46

    • A = 310


Using sine to find area
Using Sine To Find Area

  • Area of an Oblique Triangle


Find the area of the 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 problem1
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.


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