1 / 9

Understanding the Ambiguous Case in SSA Triangle Relationships

In triangle geometry, the ambiguous case occurs when you are given two sides and an angle opposite one of the sides (SSA). This situation can lead to one, two, or no possible triangles, depending on the specific values of the sides and angles involved. This overview will explore how to approach problems involving the SSA configuration, determining the number of solutions based on the relationships between the given angle and sides. Through examples, we illustrate the mathematical principles that govern these outcomes.

caroun
Télécharger la présentation

Understanding the Ambiguous Case in SSA Triangle Relationships

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. 5.3 The Ambiguous Case

  2. If we are given 2 sides and one angle opposite of one of the sides, we may not get just one answer. There are 3 possibilities … one answer, 2 answers or even no answer! The arrangement of the info is SSA Let’s think about this pictorially before trying out the math. For all these examples, we will consider being given m∠A, a, and b & we remember this was not allowed in geometry C a b A B c

  3. C b a A B c ∠A could be acute… and a < b a b a b b a or a A A A 2 solutions if bsinA < a < b 1 solution if a = bsinA No solution if a < bsinA ∠A could be acute… and a ≥ b a b only 1 solution A

  4. C b a A B c ∠A could be obtuse a a b b A A 1 solution if a > b No solution if a ≤ b

  5. Ex 1) Determine the number of solutions. m∠A = 29°, b = 31, a = 23 m∠A is acute m∠A = 132° , b = 96, a = 105 a < b 23 < 31 so 2 solutions bsinA = 31sin29° = 15.02 < 23 < 31 a b m∠A is obtuse and a > b 105 > 96 a b A 1 solution

  6. Ex 2) Solve △ABC if m∠A = 35.18°, c = 17.8 and a = 11.46 B 11.46 17.8 OR ??? 35.18° C A C and here? 180 – 63.49 = 116.51 116.51 + 35.18 = 151.69 < 180 Sure! m∠C = 116.51° Two Answers!

  7. Ex 2) Solve △ABC if m∠A = 35.18°, c = 17.8 and a = 11.46 B 11.46 17.8 35.18° C A m∠C = 63.49° OR m∠C = 116.51° m∠B = 81.33° m∠B = 28.31° b = 19.66 b = 9.43

  8. Ex 3) Solve △ABC if m∠A = 71.4°, a = 45.3 and b = 51.4 C 45.3 51.4 71.4° B A WAIT!! sin has to be between –1 & 1, so… No Triangle exists

  9. Homework #503 Pg 261 #1, 5, 7, 15, 25, 29, 34, 35, 37

More Related