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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.
When would you use the law of sines or law of cosines instead of a trigonometric ratio?
It is NOT the Law of Sines/Cosine , but the SINE / COSINE Rule. Sine Rule is SinA/a = SinB/b = SinC/c Where 'A' , 'B', and 'C' (Capitals) are the angular values. and 'a', 'b' ,& 'c' (lower case) are the side lengths opposite to the given angle. For Sine Rule, select any two terms, from the three above. This requires known values for any two angles and one side to find the other side. Or any two sides and one angle to find the other angle. Known ; angle , angle side to find a side. or Side, side, angle to find an angle. Think 2angles x 2 sides ; Cosine Rule. is a^(2) = b^(2) + c^(2) - 2bcCosA This requires three known sides to find an angle. or two known sides and an angle to find the third side. Think 1 angle x 3 sides.
