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Consider a triangle with vertices A, B and C. Call the edge opposite a given vertex by the same letter, but lower case. So side a is opposite vertex A etc.

Law of Sines says:

SinA/a= SinB/b=SinC/c

If you prefer, you can split the equation into multiple separate ones:

SinA/a=SinB/b

Sin A/a=SinC/c etc.

(there is one more part of the law of Sines which most books leave out. If R is the radius of a circumcircle around triangle ABC, then SinA/a= SinB/b=SinC/c =2R and in case you forgot a circumcirlce of a triangle is a unique circle that passes through each of the triangle 3 vertices.)

The law of Cosines says:

a2 +b2 -2abCosC=c2

or a2 +b2 -2abCosB=b2

or a2 +b2 -2abCosA=a2

Q: Law of sines and cosines in mathematics?

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Trigonometry mainly but also geometry, algebra.

Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.

Law of sines or cosines SinA/a=SinB/b=SinC/c

Having sufficient angles or sides one can use either, The Law of Sines, or, The Law of Cosines. Google them.

you must know more information. Like the lengths of 2 sides. Then using Trig (law of sines or law of cosines) you can find the remaining sides and angles.

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Trigonometry mainly but also geometry, algebra.

In trigonometry sines and cosines are used to solve a mathematical problem. And sines and cosines are also used in meteorology in estimating the height of the clouds.

Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.

Use Law of Sines if you know:Two angle measures and any side length orTwo side lengths and a non-included angle measure.Use Law of Cosines if you know:Two side lengths and the included angle measure orThree side lengths.

Law of sines or cosines SinA/a=SinB/b=SinC/c

When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.

Having sufficient angles or sides one can use either, The Law of Sines, or, The Law of Cosines. Google them.

Yes. Look up the law of sines and the law of cosines as examples. there are also formulas that can find out the area of a non-right triangle.

you must know more information. Like the lengths of 2 sides. Then using Trig (law of sines or law of cosines) you can find the remaining sides and angles.

For a start, try converting everything to sines and cosines.

If it's a right triangle, use pythagorean's theorem (a2+b2=c2) to solve it. = If it's an oblique triangle, use the law of sines or cosines (see related link)

The ACT asks questions about basic sines, cosines, and tangents. These questions can be answered without a calculator.