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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:


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

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Q: Law of sines and cosines in mathematics?
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Related questions

What branch of mathematics is concerned with sines and cosines?

Trigonometry mainly but also geometry, algebra.

How are sines and cosines used in meteorology?

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.

When would you use the law of sines or law of cosines instead of a trigonometric ratio?

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.

When do you use law of sines and law of cos sines?

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.

Altitude of right triangle with only one side known?

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

What situation would you be FORCED to use law of cosines as opposed to law of sines?

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

How do you find a missing side of a triangle without a right angle?

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

Can trig functions work on non-right triangles?

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.

How do you find the missing angles of a triangle with one?

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.

How do you simplify csc theta -cot theta cos theta?

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

How do you find a side of a triangle?

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)

Relevance in trigonometry in act?

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