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How to Calculate Degrees From Coordinates

An angle is defined as the figured formed when two legs, or rays, share an endpoint called a vertex. The rays of any angle can be transformed into a right triangle in order to find the magnitude of the angle. This transformation is done by dropping a line from the coordinate point defining the length of the upper ray down to the x-axis. The right triangle formed by this operation can then solved through the use of trigonometry, the Pythagorean Theorem and knowledge of the coordinate point values.

Instructions

- 1
  Find the hypotenuse of the triangle using the Pythagorean Theorem in the form x² + y² = h², where x is the x-coordinate, y is the y-coordinate and h is the hypotenuse. For example, the hypotenuse formed with the point of origin and the point (5, 9) is found to be: 5² + 9² = h² ---> 25 + 81 = h² ---> h² = 106 ---> h = sqrt(106) = 10.3.
- 2
  Choose an inverse trigonometry function, such as arcsin, arccos or arctan, to calculate a specific angle. The appropriate function is chosen based on what side lengths you are using to solve for the angle. For example, the leg lengths to use with arctan are the opposite length and the adjacent length to the angle being solved because tangent equals (opposite / adjacent).
- 3
  Use a scientific or graphing calculator to solve the inverse trig function using the appropriate leg lengths. For example, using arctan to find the angle θ with opposite leg length 9 and adjacent leg length 5, the function becomes: θ = arctan(9 / 5) = 60.9°

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