Mathematics, 29.09.2019 23:50 ashtonrieper1132

Describe, in detail, when to use the law of cosines, the law of sines, and the law of sines with the ambiguous case. provide general guidelines, in your own words, for each law that can be applied to any triangle situation with which you are presented. to aid in your explanation, you may refer to specific problems from the text. your response must include
the law of cosines
the law of sines
the ambiguous case (law of sines)
general guidelines in your own words that can be applied to any triangle.
at least 100 words in complete sentences with appropriate grammar and spelling.

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You can use the Law of Cosines, if only one of which is missing: three sides and one angle. Hence, if the known properties of the triangle is SSS(side-side-side) or SAS (side-angle-side), this law is applicable.

You can use the Law of Sines if you want to equate the ratio of the sine of an angle and its opposite side. This can be used if the known properties of the triangle is ASA(angle-side-angle) or SAS.

The ambiguous case is the SAS triangle. This could be easily solved using Law of Sines than Law of Cosines. Take for example: side a = 4, side b = 10, angle A = 23°. Then, we can determine angle B through Sine Law.

sin 23°/4 = sin B/10
B = 77.64°

Answer from: enriquerer12

The law of cosine can be used when the known properties of the triangle are SSS or SAS and the law of cosine can be used when the known properties of the triangle are SAS or ASA. SAS triangle is an ambiguous case, this can be easily solved by the law of sine.

The law of cosine is given by the formula:

$\rm cos \theta = \dfrac{a^2+b^2-c^2}{2ab}$

where $\theta$ is the angle and 'c' be the opposite side of the angle $\theta$ and 'a' and 'b' are the adjacent sides of the angle $\theta$ .

The law of cosine can be used when the known properties of the triangle are SSS (Side Side Side) or SAS (Side Angle Side).

The law of sine is given by the formula:

$\rm \dfrac{sin \theta}{a}= \dfrac{sin\alpha }{b}= \dfrac{sin \beta }{c}$

where $\theta$ , $\alpha$ , and $\beta$ are the angles and 'a', 'b', and 'c' be the opposite side of the given angle $\theta$ , angle $\alpha$ , and angle $\beta$ respectively.