Respuesta :
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°
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°
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:
[tex]\rm cos \theta = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where [tex]\theta[/tex] is the angle and 'c' be the opposite side of the angle [tex]\theta[/tex] and 'a' and 'b' are the adjacent sides of the angle [tex]\theta[/tex].
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:
[tex]\rm \dfrac{sin \theta}{a}= \dfrac{sin\alpha }{b}= \dfrac{sin \beta }{c}[/tex]
where [tex]\theta[/tex], [tex]\alpha[/tex], and [tex]\beta[/tex] are the angles and 'a', 'b', and 'c' be the opposite side of the given angle [tex]\theta[/tex], angle [tex]\alpha[/tex], and angle [tex]\beta[/tex] respectively.
The law of cosine can be used when the known properties of the triangle are SAS (Side Angle Side) or ASA (Angle Side Angle).
SAS triangle is an ambiguous case, this can be easily solved by the law of sine.
For more information, refer to the link given below:
https://brainly.com/question/22816520
