1 / 16

6.1 Law of Sines - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' 6.1 Law of Sines' - miron

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

6.1 Law of Sines

+Be able to apply law of sines to find missing sides and angles

+Be able to determine ambiguous cases

A is acute

A is obtuse

B

B

c

a

a

c

A

C

b

C

A

b

• 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

• Find the missing sides and angles given the following information

• C = 102.30

• B = 28.70

• b = 27.4 ft

• 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

b

b

h

a

h

A

A

• A is acute

• a > b

• 1 triangle

• A is acute

• h < a < b

• 2 triangles

b

b

a

a

a

h

h

A

A

• A is obtuse

• a < b

• no triangles

• A is obtuse

• a > b

• 1 triangle

a

a

b

b

A

A

• Find the missing sides and angles of the triangle given the following information

• a = 22 in

• b = 12 in

• A = 420

• A = 620 , a = 10, b = 12

• A = 980 , a = 10, b = 3

• A = 540 , a = 7, b = 10

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

• Find the missing sides and angles for the following information

• a = 29

• b = 46

• A = 310

• Area of an Oblique Triangle

• Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102o.

• 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.