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The law of sines states the in a triangle with sides of length a, b, and c, and angles of A, B, and C where each angle's letter corresponds with the side opposite it, that Sin(A)/a = Sin(B)/b = Sin(C)/c. The law of cosines states that for the same triangle, c2 = a2 + b2 -2abCos(C).
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Show that sin ²A plus Cos ²A equals 1?
One definition of sine and cosine is with a unitary circle. In this case, the sine is simply equal to the y-coordinate, and the cosine, the x-coordinate. Since the hypothenuse is 1, the equation in the question follows directly from Pythagoras' Law: x2 + y2 = r2, x2 + y2 = 1, cos2A + sin2A = 1. You can also derive it from the alternative definition of sine and cosine (ratios in a right triangle).
When to use sin and cos.?
The sine and cosine were originally developed for use in surveying. They provided a way to measure the distance across lakes and around mountains. Soon they were found to be useful in navigation. The sine was used to calculate pi. When electrical measurements were made, the sine law was used. If you want to know when to use the sine and when to use the cosine, you will need to get a trig book, a physics book, an astronomy book, a sailing book, and a few other books and read them all.
What are real life applications of the law of sines?
Land surveying makes an extensive use of the sine and cosine law. The idea is to subdivide the land into many triangles and to measure one side and two angels of each triangle. With the sine law the other two sides can be computed. The Mount Everest was found by this method to be the highest mountain on planet earth.
Formula for finding the perimeter of a triangle?
If you know any two angles and a side, you can use the law of sine (or law of cosine) to find the other two sides, add them up and get the perimeter. It you know the base and height, you can use the Pythagorean Theorem to get the side lengths, add them up and get the perimeter.
Is sine law applicable in acute triangle?
Yes
Show that sin ²A plus Cos ²A equals 1?
One definition of sine and cosine is with a unitary circle. In this case, the sine is simply equal to the y-coordinate, and the cosine, the x-coordinate. Since the hypothenuse is 1, the equation in the question follows directly from Pythagoras' Law: x2 + y2 = r2, x2 + y2 = 1, cos2A + sin2A = 1. You can also derive it from the alternative definition of sine and cosine (ratios in a right triangle).
When to use sin and cos.?
The sine and cosine were originally developed for use in surveying. They provided a way to measure the distance across lakes and around mountains. Soon they were found to be useful in navigation. The sine was used to calculate pi. When electrical measurements were made, the sine law was used. If you want to know when to use the sine and when to use the cosine, you will need to get a trig book, a physics book, an astronomy book, a sailing book, and a few other books and read them all.
What careers use the law of sine and cosine?
mechanical engineers, land surveyors, math teachers, and registered nurses.
What are real life applications of the law of sines?
Land surveying makes an extensive use of the sine and cosine law. The idea is to subdivide the land into many triangles and to measure one side and two angels of each triangle. With the sine law the other two sides can be computed. The Mount Everest was found by this method to be the highest mountain on planet earth.
What is snell's law for angles and velocities and wavelengths?
The Sine of incidents ---------------------------- The sine of refraction
Formula for finding the perimeter of a triangle?
If you know any two angles and a side, you can use the law of sine (or law of cosine) to find the other two sides, add them up and get the perimeter. It you know the base and height, you can use the Pythagorean Theorem to get the side lengths, add them up and get the perimeter.
What is the Lambert Cosine Law and how does it relate to the reflection of light?
The Lambert Cosine Law states that the intensity of light reflected off a surface is directly proportional to the cosine of the angle between the incoming light and the surface normal. This law helps to explain how the brightness of a surface changes based on the angle of incidence of light.
The branch of physical science that deals with the law of motion?
In physics this is called mechanics.Quantum mechanics is the branch of physics that deals with the motion of particles by their wave properties at the atomic and subatomic levels.
Damnum sine injuria?
What is Damnum sine injuria means in the Law of Torts? Give anexample of it in details.
Can the sine law be used with a acute triangle?
Yes.
Is sine law applicable in acute triangle?
Yes
When you have a right angle what does the law of cosines reduce to?
cosine = adjacent/hypotenuse
