Pitfalls in the Trigonometric Solution of an Oblique Triangle

1944 ◽  
Vol 37 (7) ◽  
pp. 311-313
Author(s):  
Irwin M. Rothman
Keyword(s):  
Complete Understanding ◽  
Included Angle ◽  
Trigonometric Solution ◽  
The Law ◽  
Law Of Cosines ◽  
The One ◽  
Ambiguous Case ◽  
Two Sides

Textbooks in plane trigonometry generally treat the solution of oblique triangles by the Law of Sines, Law of Cosines, etc. However, if one uses some of these laws without a complete understanding of their limitations, incorrect results are often obtained. The only case which most textbooks treat adequately in this respect is the solution of a triangle in which two sides and an angle opposite one of them are given, usually referred to as the “Ambiguous Case.” However, in other cases, such as the one in which two sides and the included angle are given, or the one in which the three sides are given, care must be taken if incorrect solutions are to be avoided.

Cosine Triples

1976 ◽  
Vol 69 (2) ◽  
pp. 119-124
Author(s):  
Charles G. Moore
Keyword(s):  
The Other ◽  
Included Angle ◽  
The Law ◽  
Law Of Cosines ◽  
Two Sides

This investigation of cosine triples was instigated by a chance observation. For years I have used triangles with integral sides for the purpose of quizzing students on the law of cosines. The law of cosines states that the square of the length of any side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of those two sides and the cosine of the angle between them. For example, given the triangle with sides 6 and 7, and included angle 20 degrees, the student is expected to find the remaining side using the law of cosines (fig. 1).

Sharing Teaching Ideas: Using the Law of Cosines to Teach the Ambiguous Case of the Law of Sines

2002 ◽  
Vol 95 (2) ◽  
pp. 114-116
Author(s):  
Elizabeth P. Harrison
Keyword(s):  
Triangle Inequality ◽  
Quadratic Formula ◽  
Zeros Of Functions ◽  
The Law ◽  
Law Of Cosines ◽  
Ambiguous Case ◽  
Teaching Ideas

The laws of sines and cosines easily lend themselves to links with other areas of algebra and geometry. The most-used link is probably that of congruent triangles, but additional links exist with imaginary numbers, the quadratic formula, parabolas, zeros of functions, and the triangle inequality.

scholarly journals Law and Social change: An Analytical Study

2021 ◽  
Vol 5 (IV) ◽  
pp. 01-09
Author(s):  
Dr. Shiv Pratap Singh Raghav
Keyword(s):  
Social Change ◽  
Analytical Study ◽  
State Legislature ◽  
The Other ◽  
Social Thinking ◽  
The Social ◽  
Heavy Burden ◽  
The Law ◽  
The One ◽  
Two Sides

There are two sides of each coin’ similarly. Each act of any person is also, either good or bad. And it is the rule, since existence of the society; good has to be accepted and the prohibited (evil, adharma or asatya). Indian Judiciary has generally been found to be alive to the needs of change happening in social thinking. By giving due consideration to the same while interpreting statutes in particular cases, the courts have brought out their fresh implications and thereby added new dimensions to the law. It is correct that law is an instrument of social change, law changes its shape according to the requirement of society or society changes the law through enactment of statues. In India, every session of Parliament and State Legislature introduces the Bills to amend the Act s(s) or enact Act(s). On the other hand, where, any question of facts comes before the court, judiciary’ (especially higher judiciary) is interpreting the law according to the requirement of society. The dialectic of the legal system in India, with its entrenched “multiplex of social structures” on the one hand and its multiplicity of indigenous, colonial, and developmental traditions on the other, is tremendously complex. The significant element in the interaction between law and society in India is the heavy burden on these multiple traditions and the social concerns and orientations of each.

Law’s Contradictions

2018 ◽  
Author(s):  
Nimer Sultany
Keyword(s):  
The Other ◽  
Political Actors ◽  
Political Conflicts ◽  
Other Hand ◽  
The Law ◽  
The One

This chapter analyzes concrete Egyptian and Tunisian cases that showcase the interplay between continuity and rupture. These cases illustrate the lack of a systemic relation between law and revolution. On the one hand, the judiciary that interprets and applies the law is part of the very social and political conflicts it is supposed to resolve. On the other hand, the law is incoherent and there are often resources within the legal materials to play it both ways. Thus, the different forces at work use both continuity and rupture to advance their positions. Furthermore, legitimacy discourse mediates the contradictions between law and revolution in the experience of different legal and political actors. This mediation serves an ideological role because it presupposes a binary dichotomy between continuity and rupture, papers over law’s incoherence by reducing it to a singular voice, and reduces revolution to an event rather than a process.

scholarly journals Quantification of Classified Nickel Species in Spent FFC Catalysts

2021 ◽  
Author(s):  
Monica Dapiaggi ◽  
Marco Alloni ◽  
Riccardo Carli ◽  
Nicola Rotiroti ◽  
Giorgia Confalonieri
Keyword(s):  
Zeolite Y ◽  
Complex Matrix ◽  
Spent Catalyst ◽  
Quick Method ◽  
Spent Catalysts ◽  
The Law ◽  
The One ◽  
Nickel Species

Abstract The paper presents a quick method for the quantification of nickel species in spent FFC catalysts; the quantification of known quantities NiO and $$\hbox{NiAl}_2\hbox{O}_{4}$$ NiAl 2 O 4 is first done in a matrix of fresh zeolite Y, and then in a complex matrix, similar to the one of a real spent catalyst. The method is carefully checked and the errors in the quantification are critically evaluated. After the validation of the method with known quantities of NiO, well below the law limit for direct re-use, a set of real spent catalysts (representative of a period of 12 months) is analysed. Graphic Abstract

Insider Trading in Israel and England, Part II

1972 ◽  
Vol 7 (3) ◽  
pp. 373-410
Author(s):  
Aharon Yoran
Keyword(s):  
Insider Trading ◽  
The Other ◽  
Fiduciary Duties ◽  
The Law ◽  
The One

It is submitted that even if the hapless outsider cannot bring an action for damages because of the existing state of the law regarding fiduciary duties and breach of statutory duties, he still has an equitable remedy of rescission of the contract based on quasi-contractual principles. The crime of fraud, under secs. 13 and 54, respectively, would be made the basis of setting the contract (of sale or purchase) aside. To support this proposition we shall explore the quasi-contractual principles which enable one contracting party, the victim of a crime committed by the other party in entering the contract, to defeat this contract.In Browning v. Morris, in an oft-quoted statement by Lord Mansfield, the following principle was declared: But, where contracts or transactions are prohibited by positive statutes, for protecting one set of men from another set of men; the one, from their situation and condition, being liable to be oppressed or imposed upon by the other; there, the parties are not in pan delicto; and in furtherance of these statutes, the person injured, after the transaction is finished and completed, may bring an action and defeat the contract.

Utilitarianism and the Criminal Law in Colonial India: A Study of the Practical Limits of Utilitarian Jurisprudence

1994 ◽  
Vol 28 (4) ◽  
pp. 739-791 ◽  
Author(s):  
Kartik Kalyan Raman
Keyword(s):  
Criminal Justice ◽  
Legal Tradition ◽  
British India ◽  
Local Society ◽  
Colonial India ◽  
Penal Law ◽  
The Law ◽  
Common Observation ◽  
The One

The role of legal tradition in the reformist rhetoric of Benthamite Utilitarianism presents us with a contradiction. On the one hand, there is the common observation that Utilitarian jurisprudence was necessarily ahistorical and rejected the past as a source of concepts for reworking the criminal justice system existing in Britain during the late eighteenth and early nineteenth centuries. For philosophic reformers such as Bentham, contemporary British criminal justice was to be replaced by a scientific jurisprudence, abstract, universal, and secular in outlook, and antipathetic to the more conservative insistence that the foundations of the penal law continue to be tradition-based. ‘If society was to see any improvement, its law must be reformed; if its law was to be reformed it must be burned to the ground and rebuilt according to a new and rational pattern.’ On the other hand, we find that the very same Utilitarian thinkers, in works describing the state of the law in British India, were concerned with local rather than universal conceptions of criminality. In his 1782 Essay on the Influence of Time and Place in Matters of Legislation, Bentham, for instance, urged the philosophic reformer to temper change in India by fitting Utilitarian judgments about the law to the frames of local society.

Preventive Confinement of Dangerous Offenders

2004 ◽  
Vol 32 (1) ◽  
pp. 56-72 ◽  
Author(s):  
Stephen J. Morse
Keyword(s):  
Legal Theory ◽  
The Other ◽  
Legal Issue ◽  
Central Theme ◽  
Sexual Predators ◽  
Dangerous Offenders ◽  
New Form ◽  
The Law ◽  
The One ◽  
Constitutional Regime

How to respond justly to the dangers persistent violent offenders present is a vexing moral and legal issue. On the one hand, we wish to reduce predation; on the other, we want to treat predators fairly. The central theme of this paper is that it is difficult to achieve both goals without compromising one of them, and that both are being seriously undermined. I begin by explaining the legal theory, doctrine and practice governing dangerous offenders (DO) and demonstrate that the law leaves a gap in the ability to confine them. Next I explore the means by which the law has overtly or covertly sought to fill the gap. Many of these measures, especially the new form of civil commitment for sexual predators, dangerously conflate moral and medical categories. I conclude that pure preventive detention is more common than we usually assume, but that this practice violates fundamental assumptions concerning liberty under the American constitutional regime.

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