Where sides a, b, c, and angles A, B, C are as depicted in the above calculator, the law of sines can be written as shown below. Using the law of sines makes it possible to find unknown angles and sides of a triangle given enough information. Law of sines: the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.Where a and b are two sides of a triangle, and c is the hypotenuse, the Pythagorean theorem can be written as: There are also special cases of right triangles, such as the 30° 60° 90, 45° 45° 90°, and 3 4 5 right triangles that facilitate calculations. It follows that any triangle in which the sides satisfy this condition is a right triangle. For any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. Pythagorean theorem: The Pythagorean theorem is a theorem specific to right triangles.The sum of the lengths of any two sides of a triangle is always larger than the length of the third side.Another way to calculate the exterior angle of a triangle is to subtract the angle of the vertex of interest from 180°. The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it.
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