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How to Find the Measure of an Angle in a Triangle If You Know What Size the Sides Are

The measure of an angle in a triangle can be determined with the side lengths, a scientific calculator and knowledge of the inverse trigonometric relationships. If you know only two side lengths you can use the Pythagorean Theorem, a^2 + b^2 = c^2, to determine the other side. The method explained here uses the tangent of the specified angle. However, you can use whichever trigonometric function you prefer.

Things You'll Need

Scientific calculator

Instructions

- 1
  Note the length of the side adjacent to the angle you wish to find. The adjacent side forms the "bottom" side of the angle. For example, for an angle with vertex at the point (0, 0), the side along the x-axis is the adjacent side.
- 2
  Note the length of the side opposite to the angle you wish to find. The opposite side is the one facing the angle. For example, for an angle with vertex at the point (0, 0), the line dropped down from the coordinate point above the x-axis is the opposite side.
- 3
  Use a calculator to find the inverse (arc) tangent for the values of the (opposite line / adjacent line). The inverse tangent button on a calculator is usually indicated either as "arctan" or "tan^-1." For example, if an angle has an adjacent side length equal to 9 and an opposite side length equal to 5, the inverse tangent for the values equals: tan^-1(5 / 9) = 29.1 degrees. This is the measure of the angle.

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