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.

Sharing Teaching Ideas: Ssa: The Ambiguous Case

1989 ◽  
Vol 82 (2) ◽  
pp. 109-111
Keyword(s):  
The Law ◽  
Ambiguous Case ◽  
Teaching Ideas

I have been teaching trigonometry for several years. One of my pedagogical concerns has been to be able to communicate more clearly the ambiguous case (SSA) in solving an oblique triangle by using the law of sines.

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.

Developing and Applying the Law of Cosines

2020 ◽  
pp. 274-288
Author(s):  
Vecihi S. Zambak ◽  
Budi Mulyono
Keyword(s):  
Instructional Technology ◽  
Ninth Grade ◽  
Steam Education ◽  
The Law ◽  
Law Of Cosines ◽  
Ninth Grade Students ◽  
Space Sciences ◽  
The Given ◽  
Support Students

In history, geometry was founded more as a practical endeavor than a theoretical one. Early developments of the branch portray philosophers' attempts to make sense of their surroundings, including the measurement of distances on earth and in space. Such a link between earth and space sciences and geometry motivated us to develop and implement a multidisciplinary lesson focusing on the conceptual understanding of the law of cosines in the context of astronomy. In our content specific STEAM lesson, the authors aimed to facilitate an understanding of the law of cosines in ninth grade students, and then apply the law in a star map task to find approximate distances between stars. The second part of the lesson also included the use of an instructional technology to support students' work with the star map task. In the conclusion, the authors discuss possible ways to improve the quality of their STEAM education efforts for the given context.

Proof without Words: The Law of Cosines

1990 ◽  
Vol 63 (5) ◽  
pp. 342-342 ◽  
Author(s):  
Sidney H. Kung
Keyword(s):  
The Law ◽  
Law Of Cosines

Note on the Law of Cosines

1951 ◽  
Vol 58 (10) ◽  
pp. 698 ◽  
Author(s):  
S. L. Thompson
Keyword(s):  
The Law ◽  
Law Of Cosines

Bingo & The Law Of Equal Ignorance

1977 ◽  
Vol 24 (1) ◽  
pp. 83-84
Author(s):  
Theodore Lai
Keyword(s):  
The Other ◽  
Games Of Chance ◽  
The Law ◽  
Teaching Ideas

Bingo, like other games of chance, can be used in teaching ideas of probability. An introduction to probability may begin with simple experiments using the “law of equal ignorance,” which is the basis of the theory of probability. In a fair experiment, each possible outcome has the same chances to occur. That is each outcome is as “ignorant” as the other. In an unfair experiment, an outcome is favored to occur over the other possible outcomes; the favored outcome is not as “ignorant” as the other.

Transforming the law of cosines for computational purposes

1955 ◽  
Vol 48 (5) ◽  
pp. 308-309
Author(s):  
Benjamin Greenberg
Keyword(s):  
The Law ◽  
Law Of Cosines

The law of cosines has always frustrated those teachers who wish to use it computationally. The transformation developed in this paper makes it more amenable to the use of logarithmic computation.

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