1 / 11

10-2: The Law of Sines Day 1

10-2: The Law of Sines Day 1. Essential Question: What is the law of sines, and how to we apply it?. 10-2: The Law of Sines. For these next two sections, you will need to be in degree mode In any triangle ABC (in standard notation), the law of sines states (Proof on board).

oprah
Download Presentation

10-2: The Law of Sines Day 1

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 10-2: The Law of SinesDay 1 Essential Question: What is the law of sines, and how to we apply it?

  2. 10-2: The Law of Sines • For these next two sections, you will need to be in degree mode • In any triangle ABC (in standard notation), the law of sines states • (Proof on board)

  3. 10-2: The Law of Sines • Solve a Triangle with AAS Information • Example 1: If B = 20°, C = 31° and b = 210, find the other angle measure and side lengths. • Sometimes it helps if you draw a triangle • Label it • Finding A should be obvious • Use the law of sines to find the side lengths (next slide) A 129° 210 20° 31° B C

  4. 10-2: The Law of Sines A • Solve a Triangle with AAS Information • Use the law of sines to find the side lengths 129° 210 20° 31° B C

  5. 10-2: The Law of Sines • The ambiguous case • When dealing with an AAS triangle, there’s only one solution – that goes back to your rules about triangle similarity (the same is true when given ASA and SAS) • However, when dealing with a triangle with SSA (or ASS) information, we’re left with some unknowns… ?  ?  A

  6. 10-2: The Law of Sines • Solving a Triangle with SSA Information (no solution) • Example 2: Given a possible triangle ABC with a = 6, b = 7 and A = 65°, find angle B. • Use the law of sines • Because the maximum of a sinefunction is 1, there is no B possible, and there is no triangle possible.

  7. 10-2: The Law of Sines • Solving a Triangle with SSA Information (one solution) • Example 3: An airplane A takes off from carrier B and flies in a straight line for 12 km. At that instant, an observer on destroyer C, located 5 km from the carrier, notes that the angle determined by the carrier, the destroyer (vertex) and the plane is 37°. How far is the plane from the destroyer? B 12 5 37° C A (not possible)

  8. 10-2: The Law of Sines • Solving a Triangle with SSA Information (one solution) • Example 4:Solve triangle ABC when a = 7.5, b = 12, and A = 35°. • (continued next slide) B 7.5 35° C A 12

  9. 10-2: The Law of Sines • Solving a Triangle with SSA Information (one solution) • Example 4:Solve triangle ABC when a = 7.5, b = 12, and A = 35°. • Case 1: B = 66.6° Case 2: B = 113.4° • C = 180 – 66.6 = 78.4° C = 180 – 113.4 = 31.6°

  10. 10-2: The Law of Sines • Assignment • Page 634 • 1 – 7 • 17 – 25 • 33 – 35 • odd problems • Show work

  11. 10-2: The Law of SinesDay 2 Essential Question: What is the law of sines, and how to we apply it?

More Related