How to Solve a Hyperbolic Triangle

Hyperbolic triangles are shapes that exist in three dimensional space, often wrapped around a circular object. For this reason, we can use the tools of ellipses and circles to help understand hyperbolic triangles better. These shapes are used in advanced trigonometry, calculus and advanced geometry. You can calculate the features of a hyperbolic triangle by following specific formulas.

Instructions

    • 1

      Solve the the distance of 1 radian which is the standard unit of length on a hyperbolic plane. The formula is 1 radian = 180/Pi.

    • 2

      Solve for the three sides of the triangle by using trigonometry. The hyperbolic trigonometric functions are different than the typical functions.
      sin A = sin h A/sin h C
      cos A = tan h B/tan h C
      tan A = tan h A/sin h B
      In these equations, h is the height of the triangle in radians; and A, B and C are the three angles of the triangle, measured in degrees.

    • 3

      Based on the information that you have on the triangle, input the values and solve for angles of A, B and C from the trigonometry.

    • 4

      Solve for area using the formula for the hyperbolic triangle. The formula is Pi minus angles A, B and C all times the radian squared: (Pi - A - B - C)R^2

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