multiplicity of triangles solvable purely with the law of sines

1

Law of Sines SAA/AAS 2 Angles, 1 Side ASA 2 Angles, 1 Shared Side SAS Cannot be solved w/LOS SSA/ASS The Ambiguous Case 1 0 Geometric Theorems A < 90 Acute A = 90 Equal A > 90 Obtuse a < h a = h a > h Comparison of length a to height h What type of angle is the supplied angle? 0 1 2 a > b a <= b 0 1 a < b a >= b 1 Where 2R = twice the radius of the circle in which the triangle is inscribed Multiplicity of Triangles Solvable Purely with the Law of Sines Law of Sines In a triangle, the ratio of the sine of any angle to the length of the side opposite it is equal across all three angles. OR

Upload: publicae

Post on 10-Apr-2015

276 views

Category:

Documents

1 download

Report

Download

Embed Size (px):

DESCRIPTION

A flowchart that is somewhat useful for learning how to handle the different cases encountered when solving a triangle allowed only the Law of Sines.

TRANSCRIPT

Page 1: Multiplicity of Triangles Solvable Purely with the Law of Sines

Law of Sines

SAA/AAS2 Angles, 1 Side

ASA2 Angles, 1 Shared Side

SASCannot be solved w/LOSSSA/ASS

The Ambiguous Case

11

00G

eometric Theorem

s

A < 90Acute

A = 90Equal

A > 90Obtuse

a < h a = h a > h

Comparison of length a to height h

What type of angle is the supplied angle?

00 11 22

a > ba <= b

00 11

a < ba >= b

11

Where 2R = twice the radius of the circle in which the triangle is inscribed

Multiplicity of TrianglesSolvable Purely with the Law of Sines

Law of Sines

In a triangle, the ratio of the sine of any angle to the length of the side opposite it is equal across all three angles.

OR

Multiplicity Winter 2016

PORTUGAL Sines 1H20 - PSA International · PORTUGAL SINES PSA Sines (also known as Sines Container Terminal) commenced operations in May 2004. Located 150 kilometres south of Lisbon,

Is XSS Solvable?

Two solvable cases of the Traveling Salesman …page.mi.fu-berlin.de/rote/Papers/pdf/Two+solvable+cases...Two solvable cases of the Traveling Salesman Problem G¨unter Rothe Dissertation

MultipliCITY Spring 2012

Intersection of conjugate solvable subgroups in...Intersection of conjugate solvable subgroups in ( , ) AntonBaykalov TheUniversityofAuckland Supervisors:EamonnO’BrienandJianbeiAn

Multiplicity and Memory

Multiplicity (final)

8ª PROVA DE MAR BAÍA de SINES - 2011 › events › 20110821-prova-mar-sines... · Voluntários de Sines, Capitania do Porto de Sines, Clube Náutico de Sines e Resgate – Associação

Dominance -Solvable Games

MULTIPLICITY PERSPECTIVES

Regulamento Prova Mar Baia Sines 2012 - aqualoja.net › events › 20120805-prova-mar-baia... · Voluntários de Sines, Capitania do Porto de Sines, Clube Náutico de Sines e Resgate

Exactly Solvable Models of Biological Invasion · Exactly Solvable Models of Biological Invasion ... 4.3 The problem of critical aggregation ... 2 Exactly Solvable Models of Biological

Eqs. Solvable for y

CMOS Exactly Solvable Chaotic Oscillator

Ironic Multiplicity

Climate Change: Simple, Serious, Solvable

SOLVABLE LIE ALGEBRAS - IIT Guwahati

High Multiplicity Study

MULTIPLICITY CONVERSATIONS

Município sines

EXPLICITLY SOLVABLE KIRCHHOFF AND.pdf

Multiplicity Codes

Multiplicity Winter 2015

Solvable, Hyper-Multiplicative Equations Over

Explicitly Solvable First Order Diﬀerential Equationsmzhan/chapter2.pdf · CHAPTER 1 Explicitly Solvable First Order Diﬀerential Equations ... 2 1. EXPLICITLY SOLVABLE FIRST ORDER

INSEPARABLE FINITE SOLVABLE GROUPSInseparable supersolvable groups are p-groups, as well as inseparable solvable A -groups and p-nilpotent groups. However solvable, but nonnilpotent,

Solvable Stochastic Control and Stochastic …Solvable Stochastic Control and Stochastic Di erential Games Tyrone E. Duncan University of Kansas February 2016 Tyrone E. Duncan Solvable

5 Maximizing submodular functions Minimizing convex functions: Polynomial time solvable! Minimizing submodular functions: Polynomial time solvable!