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How to Use Trig Functions to Find Angles

To find the unknown angle of a particular triangle, you use the three primary trigonometric functions: sine, cosine and tangent. As long as you know the lengths of the triangle, you can use these functions to find the size of the angles. Finding the angle becomes a matter of plugging the information into the proper equation.

Things You'll Need

  • Measuring tape
  • Calculator
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Instructions

    • 1

      Assign a letter to each of the sides, such as A for the vertical side, B for the horizontal side and C for the hypotenuse. Measure the length of the three sides of the triangle using the measuring tape if it is a real-world problem.

    • 2

      Decide on which angle you want to find and assign that a variable as well, such as angle D. Plug the values of the sides into the equation for your choice of the trigonometric functions. The sine is the opposite side of the angle divided by the hypotenuse. The cosine is the adjacent side to the angle divided by the hypotenuse and the tangent is the adjacent side of the of the angle divided by the opposite side of the angle.

    • 3

      Calculate the decimal values of the angle by diving the sides of the angle for the chosen trigonometric function. This the the angle in decimal form. Multiply the answer by 360, the total degrees in one full rotation, to find its degree equivalent. For example, the decimal angle D is .25 and multiplied by 360 becomes 90 degrees.

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