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pjhphysics
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If I know the length of all three sides of a triangle and the coordinates of two of those points, how can I find the coordinates of the third point (in a scalene non-right triangle)?
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To find the third point of a scalene non-right triangle, you can use the distance formula to calculate the distance between the two given points. Then, using the law of cosines, you can find the angle opposite the unknown side. Finally, using trigonometric ratios, you can find the length of the unknown side, and then use the distance formula again to find the coordinates of the third point.
No, the Pythagorean theorem only applies to right triangles. In a scalene non-right triangle, the three sides have different lengths and the angles are not 90 degrees, so the Pythagorean theorem cannot be used to find the third point.
Yes, it is possible to have more than one solution. This can occur when the given side lengths and coordinates of the two points create multiple triangles that satisfy the given conditions. In this case, you will need to use additional information, such as the location of the triangle in relation to the coordinate plane, to determine the correct solution.
Yes, there are two special cases to consider. The first is when the given points are collinear, meaning they lie on the same line. In this case, the third point can be found by extending one of the sides to the desired length. The second case is when the given points form an isosceles triangle. In this case, the third point can be found by reflecting one of the given points across the line of symmetry.
No, the law of sines only applies to triangles with at least one known angle. In a scalene non-right triangle, all three angles are unknown, so the law of sines cannot be used to find the third point. The law of cosines, which does not require any known angles, is the appropriate formula to use in this case.